The most important and the most useful tip in learning calculus is to do your homework. As simple as it sounds, many people find that homework is not necessary to do until the last possible moment. This creates extra stress when you are trying to get the homework finished before class starts, extra stress that you do not need because calculus is already hard enough.
Be sure to know and memorize your basic derivatives and rules for differentiating. You should be able to recite from memory the power rule, the product rule, the chain rule and the quotient rule. You should also know the derivatives of functions such as exponentials and logarithms.
When in doubt, talk to your professor. All professors have office hours posted in the syllabus, outside of their office or on the course website. Professors have to teach to a classroom many students in lecture, but one-on-one time with professors can be quite helpful.
The most common mistakes in calculus are not calculus mistakes but algebra mistakes. Learn how to factor and simplify problems. For example, why use the quotient rule when you can use the chain rule?
Finally, the adage "practice makes perfect" applies to mathematics as well to sports. Oftentimes, professors do not assign enough homework. To remedy this, just open up your book to the chapter and start doing extra homework for practice and check the answers to make sure you have done them right.