R.M. pretty much covers it and Nephas gives two great examples.
There are things you can learn, and things you cannot learn. It all comes down to the available equipment and how well you can use it. Learning, in most animals you are familiar with, is a function of the CNS. In very simple terms, there's neurons, lots of them...those are your guys. They can get excited or inhibited and, in doing so, they can affect other neurons with their behaviors.
Let's make this very simple. Think of neurons as individuals you are trying to synchronize in some way. Let's assume they you are trying to have them sing along to the same clear cut frequencies, i.e. synchronize them in terms of pitch, or sing in unison. They will definitely need to work through a few dozens of problems:
a) Some of them will not know how to increase or decrease the pitch. You will have to teach them. They will produce random sounds and you will mark them on a grading scale from low to high, so that they, at least, understand the ordering. You don't expect them to know in advance what an A or a B note means. You have to let them randomly produce pitched notes and teach them, for example, that "this sound you just made is quite close to a B", or "that one is in between a C and a D, lower this a bit and you're C".
b) Some of them will not be able to hear themselves, they will be deaf. You will have to find a way to teach them that a higher pressure (sort of) in the area of their airways means a higher pitch. Then you will need to calibrate them, i.e. teach them that a specific magnitude of pressure corresponds to the note you want to achieve. This is tougher because their self-feedback will be coarser. They will need to "map" a narrow range of roughly and empirically quantifiable pressure magnitudes to some symbols indicating they are right. And then they will have to do this backwards, to sing, i.e. reproduce the pressures based on the symbols. Most of them will be hitting the notes as, e.g., C ± a "few" Hz (that is, if you're lucky).
c) Some of them will have a "resolution" problem. Usually, people can distinguish pitches that differ by as little as 3.6 Hz in between 1-2kHz. Some of your people are going to do worse, they will jump in steps of 10s, or 100s of Hz. They may learn to fine-grain their control but it will take time, so now you will have to make do with some "weak links" of, again, a C ± some tens or 100s of Hz, which may, or may not be important. A middle C is at 261.63 Hz and one octave above is double that value. You certainly don't want someone able to jump in steps of 80Hz in their sounds, or you'll only get ~3 scrambled notes in that octave.
d) Some of them will not understand you, because you don't speak the same language. You will need to do something special with them, you will probably need to show them the symbols, let them start raising their pitch, and have someone actively touch them to stop the raising when they hit the right note.
e) Some of those people (even many), will generally be impossible to work with, so you will need to send them off to do something else.
f) ... various other problems...
This would be "systematic" learning, and it takes a lot of time until you can produce a tolerable choir out of that many people. For some things that you need to learn, there is simply no shortcut. You need to learn how to recognize lots of symbols, match them to meanings, symbol combinations, operations, then meanings again, then how meaning combinations give you other meanings... think mathematics, physics, etc, you can't just dive directly into integrals or particle physics and expect to learn anything. But, like the people you are trying to orchestrate in the example above, your neurons may be better suited to those tasks. You may have fewer noncompliant neurons, lots of responsive neurons, more high-resolution neurons, etc.. Neuron capabilities are like your inner "vocabulary" and think about how it would be if you had a 25-letter language. It wouldn't make your life totally miserable, but you certainly would miss on lots of words, let alone some letters might switch off more important words from your vocabulary than other letters.
Now, here comes the newsflash... for the most part, that's not how the brain learns (but at least, it gets someone to appreciate a high-level approach to learning). You don't really have access to neurons and you certainly don't control them at the microscopic scale. What does happen is this:
Some areas specialized in expressing intentions or reflexes initiate a rough signaling cascade.
The cascade travels through various neuron groups, being processed along the way (i.e. some stop firing, others fire harder, others inhibit their senders, others cease transmission, etc.).
The overall signal cascade has some terminal effect, external (action) or internal (introspection). A return signal, along with certain adaptations begins to unfold "backwards" based on the terminal effect. Some neurons will increase their transmission threshold, they will require more excitation to fire. Some neurons will begin to filter their response, e.g. by ceasing transmission when signaled by some specific senders, but not by others, or even magnifying the signal when signaled by specific ones.
This whole filtering goes back and forth until some sort of balance is achieved, which has a terminal effect that is precisely the one you like to have, based on the applied necessity (of course).
Doesn't make sense? Let's go back to your individuals! Blow systematic learning. You will learn in chaos! Start producing a note and have them all do the same and produce a note, any note. Tell them to try to mimic your note. Because of how (healthy) ears work, an observer can easily tell that they are actually listening to two different tunes, if you are not in unison. Consonance is a quality that can be "felt" and matching the tunes in terms of pitch can be further self-guided by exploiting the fact that dissonance is easily perceived, but also, as tunes approach each other in terms of pitch, because of various phenomena, such as interference beats, you can use the "annoyance" feedback to tune up or down, to eliminate those and achieve a single uniform auditory effect.
In short, because of being able to compare the produced result to the desired result (or, more usually, to the undesired results) and fine-tune it accordingly, it is possible to iteratively approach the desired result, and this is, in a sense, the actual way that the brain learns. Thus, broken down, learning actually requires the following capabilities:
- Intention to produce an effect.
- One (or more) effector mechanism(s) to produce an effect.
- Ability to quantitatively or qualitatively compare the effect to the desired effect (assessment).
- Ability to make small adjustments to the produced effect by adjusting utilization patterns of the mechanism, in a way that can be used to "steer" the utilization patterns in order to produce the desired effect.
You can apply this looping pattern to pretty much anything you learn. Lack of any of those mechanisms means you cannot learn. As an example of this, think about learning how to write with a mechanical pencil.
You need to hold the pencil and apply a very specific force in a very specific order of directions, timely synchronized, so as to appropriately overcome the friction between the tip and the writing surface, only by just as much as necessary, so that you can sustain a given progression of "rolling" speeds of the pencil tip, which would produce the desired scriptures (let alone you need to know the actual shapes you are trying to scribble). In the process, you need to refrain from applying excessive force, to avoid breaking the tip. Imagine, for a moment, how many parameters you are dealing with:
Holding the pencil is of utmost importance. Even tiny changes in angle between the tip and the writing surface will affect the produced friction and you will need to readapt the forces you are using to drag the pencil. Holding the pencil at a different height will also change the force you need to apply at the anchor point, in order to produce a given force at the tip, because of the effect of the lever arm on the torque. The desired force at the tip is practically constant for a given writing surface, but holding the pen a couple mm lower might make you break the tip (because of the increased force at the separating surface).
The "threshold" of breaking is very delicate and the margins of usage too small. Also, different surfaces have different friction coefficients, so those delicate margins might make you break the tip while "readapting" to a different surface. You need to be able to adjust your applied force with a very high resolution, having the ability to increase/decrease it at will in very small intervals/jumps, certainly far lower than the total applicable range (between the minimum force needed to only just about "roll" the tip, and the minimum force that would break the tip).
You also need to avoid tip retraction, so the vertical component of the applied force is also something you need to watch out for and has equally small effective range and usage margins.
The utilization mechanism, the "effector", in a sense, is the coordinated movement of your muscles. You don't really know the complex vectors of the forces your muscles are applying, you only know the net force and, even this, is not one, but multiple, applied at the various locations of touch with the mechanical pencil, as you are not only touching it at a single point. You need to learn how to coordinate your muscles to apply very specific forces in very specific directions, which will sum up to a very specific set of forces in the contact points. This problem can readily be compared to a subset sum problem, or the generalized knapsack problem. The only thing you need to know about those is that they are notoriously infeasible when the input is large and so is the coordination of the so-many muscles of your hand and fingers, and the degrees of freedom that their combination brings into play.
The process itself can be decomposed into the signals between the neurons in your brain, firing in an orchestrated manner, so that specific forces can be produced (and continuously readapted in real-time), which will provide the very specific effect. For this, the neurons need to learn just how much to fire (and this includes a whole other world of parameters involved) but, in general, because of the sheer number of neurons, the number of potential "firing" combinations (i.e. ways to "orchestrate") is unimaginably enormous. When you get some of the (admittedly very few) ways of "proper" writing, which please you, you can repeat them, so that the specific "orchestration" is reinforced, while the wrong ones are "weakened".
As you have probably guessed, thus, learning how to write is, in effect the process of learning millions, if not billions, of ways of how not to write, until the way you write finally approximates something that pleases you (or your teachers!). The time you need to explore all possible "orchestrations" is, of course, going to be large, but also, highly dependent on the built-in qualities of the neuron networks.
You can also consider the example of 2-point orientation discrimination (2POD). The minimum discernible distance of two points apart, touching your skin generally depends on the location. The reason for this is multifactorial but, in simple terms, is related to the "equipment", i.e. how many nerve endings are on the area of the skin, what types of cells, and, of course, how much volume of the brain is dedicated to it, as well as to how well-prepared it is to handle that.
Therefore, to answer your question, how easy it is to learn something actually depends on how complicated it is (i.e. how many parameters are at play), how effectively you can employ your learning loop and, of course, how strong and well-prepared your "infrastructure" is. If you actually "degrade" some parts of the brain, you may lose some important functions (e.g. prosopagnosia). If you connect areas together, which were not connected before, you can create new (sometimes rather funky, even mystical) functions, such as synesthesia.
Taking all of the aforementioned into account, you can easily look for sensory strengths of other animals. The usual comparison would be olfaction, as sensed by, for example, scent hounds. Learning to sense, identify and distinguish smells is easier for them, because they have much more suitable infrastructure for this specific function.
Finally, you could always make the notorious comparison of a compute to a form of "life". One that you can "program", so that it learns to do exactly what you teach it, doesn't ever forget, and is capable of learning tremendous amounts of instructions over a few seconds to minutes (think copying files, installing applications, etc.). Do not forget Clarke's 3rd law, too!