The following article contains some great resources for getting started with Mathematica and the Wolfram Language: http://support.wolfram.com/kb/30451
For a more thorough introduction I might recommend An Elementary Introduction to the Wolfram Language. It's a free online book which has everything you need, including exercises, to get started with the language.
We also have the Fast Introduction for Math Students tutorial which more directly covers a lot of the topics you might need for a calculus class.
Mathematica is a great tool to accompany your studies in mathematics and other fields, and getting practice early in it is certainly worth your time. Good luck!