It really depends on how far you want to go
Do you want to create a number of believable sounding words, write foreign sounding sentences or construct a language very different from your own with its own vocabulary, grammar and history?
All of these require very different levels of effort. At the very lowest level we have:
Creating a naming language
A naming language is simpy a number of coherent and realistic-sounding words with which you can name the characters, places and items of your world.
A naming language has very little grammar, although you may need to distinguish adjectives and nouns.
So how do we make it sound realistic and distinct from English?
We start with a sound system, the core sounds of our language. A useful tool for transcribing sound systems is the IPA.
We'll start with consonants:
Consonants can be defined as on a matrix of place of articulation and manner of articulation. Place of articulation can be between the lips (bilabial), between the tip of your tongue and your teeth (dental), between the roof of your mouth and your tongue (velar), etc.
Manners of articulation can be types of consonants like plosives (/p/, /t/, /k/) or nasals (/m/, /n/, /ŋ/) but can also be the same type but with a distinguishing feature such as voice (meaning your language would also have /b/, /d/ and /g/) or perhaps other features such as palatalization or labialization.
What's important here is for that matrix to be mostly filled out. Every natural language has most but not all of its matrix filled out. Basically all natural languages have /p/, /t/, /k/, /m/ and /n/.
In terms of vowels, pretty much no natural language has less than /a/, /i/ and /u/, most have something like /a/, /e/, /i/, /o/, /u/, whereas some have a lot more. This chart shows some good examples.
Vowels may also have various qualities such as length (which is not the same as "long" and "short" vowels in English) or nasality (like in French). These qualities need not and usually don't apply to every single vowel.
For either, I think going onto Wikipedia and looking at the sound charts of some of the world's languages gives you a good idea of what a natural language does.
Now, onto what really makes your language sound distinct:
Every spoken language has rules as to what can be a word. That's why you'll register "trhnrbth" as just me mashing on the keyboard.
Words are made out of syllables and syllables have structures whose rigidity depend on the language. Japanese, for example only allow syllables with either a single or no consonant as an onset, a vowel as the nucleus (center) of the syllable, and then it may only end on a nasal.
That gives us (C)V(n) as our syllable structure.
The more we allow into a syllable (something like CCCVVCCC, for example), the more rules we actually have to give to what is allowed to cross over.
In English, for example, whenever /n/ is followed by /k/, it will be pronounced /ŋ/, because the two latter sounds are both velars and easier to pronounce together.
Sounds may also merge into new sounds which only exist in those contexts. A good example is how "sugar" is pronounced /ʃөgә/ rather than /sjөgә/, as the /s/ and the /j/ merge into /ʃ/.
If you set specific rules as to which sounds are and aren't allowed together in your language, this will make it distinct from other languages.
If you're creating a writing system for your language, taking into account what your speakers percieve its sounds as will inform how it will be spelled.
So if your syllables are restrictive, perhaps they would have a letter for each syllable, whereas if a lot of sound occur from merges of several different other sounds, perhaps it will be spelled as those original sounds together.
The second level is:
Creating a language with grammar
Obviously, the easiest way to do this is simply to take every English word you're using in a sentence and make up a word in your language to replace it with.
This is however not very interesting. What makes languages interesting is what makes them different from eachother.
To start with, you need to define your language typologically. Is it analytic or is it synthetic?
What these words really mean is if a language uses a lot of modifier words around the core words of a sentence or if it modifies its core words with affixes.
English is a very analytic language whereas Inuktitut is sometimes considered polysynthetic:
Tusaatsiarunnanngittualuujunga. - I can't hear very well.
Among synthetic languages, there are agglutinative languages, which use several single purpose affixes on words, aswell as fusional languages which use only one or two multipurpose affixes on words.
Note that every language is part of a spectrum (not just squarely agglutinative) and that within every language there is a spectrum of functionality which resembles all of these typologies to some degree.
After that, you have mandatory markings on words.
English, for example, marks every noun with article and number. A word like "places" is in the indefinite article plural. Not every language marks number and not that many mark article.
For verbs, for example, you could, along with tense and aspect (which English already does), mark evidentiality, whether or not the speaker saw what happened or heard about it.
Looking through grammatical categories on Wikipedia is useful for finding grammars very different from your own language.
The third level would be:
Creating a language history
Languages evolve from other languages and it shows. Usually, irregularities come about from various sound changes playing out.
I've already written an answer on precisely this topic, so I'll simply refer you there.
I will however elaborate on why this is even if you aren't going to reveal your root language in whatever you're showing your finished language.
It clearly shows when a language has repetitive forms, which makes it more realistic. That those forms also aren't just the same ending tacked onto different roots, but is rather changed in some form, shows even more realism.
Creating a language history also allows you to create dialects and language families really easily, as all you need to do is give them different sound changes from eachother.