The online help and documentation with Mathematica is one of the best for any program I have ever used. Use it frequently. There are a bunch of good tutorials built-in. You should go through the ones on basic symbols, algebra, and differential equations, as well as any others related to your specific interests.
Because Mathematica is a really huge software system and speaking from my own experience with it, the best way, is to use it in a regular basis dealing with some specific topic and/or a specific area according to the problem at hand and expand to other areas as well as time goes by, in order to develop a sense of the "big picture".
There are books with for problem solving using mathematica. I suggest you search for one of them. There's no better way to learn a software than to solve problems using said software.