How do I deal with calculus? I go to class, don't take any notes, do one or two questions before the test and get perfect. Does that help?
Seriously lots of people struggle with calculus. I tutored tons and tons of people in high school.
Precise limits? As in lim x->n where n is finite? Like lim x->5 (x^2 -6x + 5) / (x - 5)?
Do you know l'hopital's rule? hehe... it is a nice way to "cheat" if they haven't taught it.
I've found that one of the most important things for people who struggle in math is for them to know that they're not alone. Not many people will admit that they need help, but a lot of times when they see me helping other people, they don't mind chiming in too. In my last year of high school even the top students would ask me for help and a lot of them had egos the size of jupiter. People like reinforcement.
Do questions that you know how to do and then build on the ideas from those and try harder questions. If you need help at that point then get it. Use a consistent 'attack pattern' for every question so that even if you don't get the answer you will always set things up to get some partial marks.
DON'T ask questions in class. This is the path of no return, really. The way I work in a math class is I just sit back and watch what the prof does and I will only interrupt when he does something wrong. And I make darn sure he's wrong before I do. Usually you can catch a prof once or twice in a class if you're careful. This is my way of making sure that I understand the material 100%. But don't ask for clarification because it's just not the appropriate forum for it. Wait until after class to talk to a prof or TA or your friends.
If you can master polynomials and rational expressions, calculus should be an easy next step. Limits just describe how those functions behave. Derivatives just let you analyize local extrema which again lets you determine how they behave, where they are large, small, etc. Integrals allow you to find the area underneath a certain range of a function. (EDIT: Okay well derivatives are good for concavity and points of inflection and all that fun stuff too, not to mention all the applications I left out)
If you can master those things you've got a good understanding of the fundamentals of calculus. Well, those things + pythagorus + trig identities....

And FACTORING. Lol