Many answers so far identify the primary issue as social/cultural, but none feel like they hit that aspect squarely. I started thinking about it, then realised that the book "Connecticut Yankee in King Arthur's Court" was actually the prototype for a good answer. So I'll draw freely from that book, below.
Your problem is that your aliens are a small group of outsiders, in a medieval setting. They want to quickly pervade society with completely new ideas and inevitably, also with major social implications. For a handful of beings to change a whole society's technological and social basis, it has to overcome huge inertia. That was the issue which ultimately destroyed the protagonist in Mark Twain's story. So we need to do better.
And we have a year to do it, for the OP....
That said, I think Mark Twain's protagonist had the right idea. It was just executed without thinking enough about the massive upcoming backlash.
Medieval society is top down. Like many modern dictatorships, it's a "strong man" hierarchy. Seizing the top, and consolidating an iron control over the layers below it, is essential to any new pervasive knowledge, skills, or change. Your aliens can do this; they can detect and monitor society far better than Twain could have realised, and we can assume them to be socially competent and have many many more ways to head off a troublemaker, than just execution. Twain used ridicule, we could think of many ways to remove possible flashpoints and figureheads, and awe the society so much that rebellion doesn't happen. That includes bringing them to describe what's happening and its benefits (genuine reeducation, not the Chinese version!), finding their priorities and marketing the changes to them in desirable terms, offering them power or safety (we don't care about lower power levels so why not), flooding society with miraculous information - a visual broadcast in every town and village, a holographic alien projection in charge of every settlement, the image of the alien council in the sky from all parts of the country.
In short, control the top, and ruthlessly awe and dominate the rest. Install those willing to follow in the top layers below you and remove silently all opposition (education or death, you choose). Do whatever is needed, so that you can direct that a given action, or social practice, will happen, and be sure it will, regardless whether it seems confounding to the existing people. Then and only then, will you be able to promulgate all the skills and technological bootstrapping, you need, as fast as possible.
That will be your fastest way. Much faster, and much more certain, than trying to convince people to do weird non-traditional stuff in towns and villages across the country. Take control, dominate, and place yourself in a position where you can make such directions and be sure they'll happen. Then, when you do, it will already be a social norm that "we do what our overlords say", and inertia will be far less an issue or not at all, in practise.
Order of teaching
I've divided this into three areas. They can all be done in parallel.
Control can be fast. Really fast. Once you have sure control, you can rely on it to skip steps, or do things in parallel. For example -
- Mining certain ores: You'll need those for manufacturing, as well as for products. Think of having the right kind of raw materials in production for steel, for furnaces, steel, and the start of mass production - tools and transport.
- Producing relatively pure water: Not for health, but again for manufacturing. The OP focuses on teaching technology not healthcare. You need basic raw materials for that, and water that's relatively clean is needed in many industrial processes.
- Furnaces: The major forms of mass production will need furnaces in their supply chain - think quick ways to produce glass, metals, and later, for welding or power production.
- Transport/logistics: You'll need to task a part of the population with transport, until you bootstrap to a point of having reliable tools, and basic engineering for things like wheels and profiled steel.
What is interesting is, if the aliens vanish, those types of industrial precursors will probably continue to be maintained so long as social order exists. They really are fundamentals.
A second stream will be education. If you just focus on teaching, and leave aside any implementation, your aims crudely are (1) to get key knowledge out there and saturated in society, and (2) a smaller group of advanced scholarship/knowhow underway.
My rationale here is that changing healthcare, education etc is a huge slow undertaking and won't meet the OP need of technological improvement within a short time. What's much better is to teach many people a 6 month crash course in knowledge and knowhow - then send them back to their communities, where they can autonomously use that knowledge as they see fit. The knowledge will pervade much faster, and be used in particular for goals that you set, and actual societal needs.
So for example, you teach hundreds of people, high school (16-to-college) mathematics, or basics of medicine/sanitation, or essentials of chemistry and physics, or principles of engineering, and an overview of basic technologies (tools, power generation, etc). Then send them away and teach the next batch.
The knowledge will pervade and be used towards your goals, without draining your resources to implement a medical system or educational system. The systems will spontaneously arise if you educate widely.
Of note - writing takes time to learn. Most people aren't literate. You don't have time to fix that. Use AV or VR or holograms or verbal teaching instead, for now. I don't think printing will help you for the while, as you are trying to teach such new concepts that a book won't help. Better to teach and develop things initially at least, by showing and by training, not by circulating books.
3) Societal structures for technology to develop
Last, you'll need some basic structures. We use corporations and government established bodies as vehicles to do works. Your society doesn't have those and will need them, or something like them. Meaning, they need a way to mobilise wealth and cooperation, to establish engineering companies that produce basic tools and components, basic sanitaryware, basic products and services of other kinds, standardisations as needed.
Fortunately you control the hierarchy. You order it so.