What are the different options to study UX DESIGN? Specific degree or formation? can we do a home study?
There are many academic programs that will result in anything from a certificate to a PhD. Human Factors International (HFI), a for-profit UX training and consulting firm, has a good list on their site:
There are also certificates that you can earn by taking an exam. Training for the certificates will provide you quick exposure to the field, but will not make you an expert on UX immediately. This will only come through work experience and mentoring. Here are a couple of those certificate options:
Like others, I recommend diving into the UX literature. Everyone has their own favorites, but I would start with "The Design of Everyday Things" by Norman, "Don't Make Me Think" by Krug, and "A Practical Guide to Usability Testing" by Dumas & Redish.
Finally, I would get involved in any local chapters of national groups like UXPA, ACM SIGCHI, IxDA, IA Institute, etc. Through those channels (or via your own workplace), I would identify a mentor locally to help you start your career in UX.
Although the class is now 3 weeks in, Stanford is running their Intro to Human Computer Interactions class online through Coursera:
This is the second time it's being run, and I imagine it will be run again in the future. The class is a great introduction to designing an actual product, starting with observing users and looking for problems to design for, all the way through testing a functional prototype. I took the class both in person at Stanford as an undergrad, and I'm taking it right now through Coursera (it's a great refresh of the content!). I'd highly recommend it.
The best advice I've ever received regarding UX education:
Find good books in the industry and read them -- cover to cover. Ones I've found particularly useful include The Design of Everyday Things for theory, About Face for "soft" techniques, and Quantifying the User Experience for "hard" techniques.
The best thing you can do for yourself is practice. Practice the things they talk about, and soon enough you'll know them by heart. Classes can teach you a few things, and there's good reason to complete up to a master's degree. But it doesn't seem to matter what you complete, just that you have a degree and that you're good at what you do.
Join some organizations and meet people. UXPA is a good one that I'm a part of here in NYC. It'll help you get a sense for what people are actually doing in the industry. And yes, @Aadaam is right: read this site.
Here's a great article that helped shape my thinking when I was in the process of breaking into the industry: How to Break Into UX Design.
You can study UX design all by yourself (as with any other subject in web design). You can easily be self-taught but it depends on your ability to execute the UX process and the outcome, to be a good UX designer.
However, and to be very specific to your question, there ARE courses provided by universities. They usually call it: Human-Computer Interaction. In there you will learn how to carry out user research, focused groups, learn more about user psychology, social studies, document your finding, etc... This is all very useful and it is really what UX is about.
As an example, my university offers a Master's degree on this:
Besides adrianh's answer, I'd alsorecommend reading UX.SE (this site)
Even if you don't answer the questions, it's important to think about them.
In the real UX world, a lot of different issues come up in seemingly unexpected ways. Some of them end up on this site. You can never know when will you need to design an Android app (even if you work on WebApps), or make a huge intranet application more usable (even if you're focusing on consumer products right now)
So I guess it's pretty fine and gives you a lot to learn if you try to step into the questioner's shoes, and click on the Balsamiq button to try to create a solution, or try to trace the issues back to primary UX values.
Even if you find out there's already a better answer than yours, or you find out that you don't know the answer, and you don't hit the Post Your Answer button at the end, it's an amazing learning opportunity.
People come to the UX world from many different places. Some from design degrees, some from UX / HCI type degrees, some from cognitive psychology, others from CS, others from other weird and wonderful vocations.
All get good at UX work by actually doing UX work. Degrees, books, blogs, courses, etc. are all great - and impart lots of useful information. However, like riding a bike or learning to draw, you don't get good at UX by being told about it or reading about it. You get good at it by doing it.
So if you're looking to get into the field by all means find a degree or course you can start learning relevant facts, skills and techniques - but most importantly find a way to start practising and applying that knowledge.