The Wolfram Language documentation is on-line and it s good place to start to get a sense of the breadth of the language–but be careful not to be overwhelmed by that breadth: I will lead you along a path that gets you going and which lets you independently continue to evolve your knowledge of it. (The documentation on the web is static; however the version of the documentation that is contained within Mathematica itself is live: you can use it to experiment and learn in situ.)
Wolfram Research has an archive of a variety of screen casts that are worth exploring.
The Wolfram Demonstrations Project is a repository of (as of the date I am writing this) nearly 10,000 examples of user interfaces written in the Wolfram Language by users themselves. Each of these can be downloaded and used with the free CDF Player. The WolframLanguage code that was used to create them is included, so you can learn from them. These were created using Mathematica but are deployed as CDFs so that anyone can use them. One possible goal for a student is to create a demonstration for a topic that they are interested in and submit it for publication in the Wolfram Demonstrations Project. In the Mathematica Summer Camp (http://mathematica-camp.org) this was what the students did during their 2 weeks of intensive work.
Wolfram research offers a variety of on-line (and occasionally in-person) courses about their technologies. Look here for their offerings.
So... you may wonder why am I putting up a link to a potential competitor! There are two reasons. First is that what I am offering is the one-on-one experience of learning the Wolfram Language with customized exploration of your research interests: we are going to explore your ideas and projects together in a guided fashion. Second, "any port in a storm." I want you to use all the resources at your disposal to learn the Wolfram Language–ultimately I will be one part of that process. But find any others that fit your needs and combine them with my help in whatever way suits you best. And bring to me any questions that come up during those forays... let's answer them together.
The Wolfram Community is an on-line forum where users of the Wolfram Language can ask simple or sophisticated questions and other community members respond. I often answer questions there and you can see some of my responses at this link: http://wolfr.am/Y9poHr. By the way, I made that shortened link (the original one is quite long and unwieldy) using the Wolfram Language function URLShorten.
An older on-line community is the Mathematica Goggle group ("MathGroup"). Currently it is not active (and it has largely been replaced by the Wolfram Community). But you can see some of the questions that I have answered (and asked!) over the years at this link: http://wolfr.am/1lIczy8.
For a view of advanced questions and answers about the Wolfram Language take time to look though Mathematica Stackexchange.