Step 1: pick a C compiler. There are numerous ones out there - the most common on 18F's is Microchip's own C18 compiler. BoostC is another option.
Step 2: go to the company's website and look at the documentation for the compiler you have chosen.
Step 3: do some google searches and find example code for the compiler you have chosen.
It's hard to answer your question about integration on the PIC. Floating-point math is a nightmare, but in certain applications you can get away with 'good enough' integration using integer math (like for PID control systems where the precise value of the integral term is not extremely important and errors don't really compound over time due to the nature of the system). Without knowing your specific intents it's impossible to say.
Since you've never used PICs and are attempting to dive into the more complicated 18F's, you had better budget in a lot of time to your project to learn the ropes, and be prepared to do a lot of searching, reading, and research, or you may be unpleasantly surprised at how quickly you end up in over your head...