One of the challenges in becoming a math major is learning the art of mathematical proof.
It is proof that distinguishes mathematics from other academic disciplines, giving our subject a permanence and transparency which makes mathematics truly timeless. Most students come to college having already exposed to a wide range of logical thinking processes, even if they haven't been aware of them. Being able to phrase and support logical arguments, however, is a skill that takes time and effort to master. As with any new skill, it will be your commitment to frequent and careful practice that will turn this new technique into second-nature.
As you transition into a proof-based class, your best resource is the professor of your class; this person can help you learn to read and write mathematical statements, and they can give you tips on how to approach certain standard proof practices. There are also a number of books which help students understand the basic structure of proofs. This PDF was a short guideline written by Erica Dohring ('14) which gives some ideas for how students might effectively transition into a proofs-based class; it also includes some suggestions for further reading as you explore this exciting new mathematical frontier.