Get the zlib source code.
I really don't want to hold your hand all the way. Part of programming is learning how to learn properly, so try to keep up. In a professional environment, you'll have to use other libraries, and this is a good first step.
Use the source code as part of your own project, save for the samples that define the main() function.
It's important to
, it's the header that contains the information you need as far as functions and structures you'll be using.
Keep it as simple as you can. A simple compression stream and inflate/deflate functions to get you started.
Remember that this is ONLY a compression library. Unless you're using the gzip functions, you'll have to provide all 'outside' information such as file size, compression start and end markers, and number of files compressed yourself with the packaged data. You'll have to be organized.
I also want to suggest that it's not a good idea to try to make your own compression algorithm. You'd be going in the wrong direction. After all, nobody's going to re-make all the low-level microsoft systems themselves by hand simply because they don't want to learn how to use their client-sided functions.