First, you should find the FAT specification. Google is your friend.
Second, you should find a disk image that is already formatted and (heavily) used with this FAT file system on it so that you can extract information from it. See how it is put together.
Something I did when I first started, and I strongly suggest, is that you write a small utility that will view the MBR, BPB (BIOS Parameter Block), and/or other parts of the file system in question. Dump the contents of an already built file system.
I use WinXP as my development system. You can see what I am talking about at
http://www.fysnet.net/win_dump.htm. You should do the same using whatever development system you are using.
With the specification sheet and the extracted information both in front of you, you should be able to see exactly what the file system does and how to implement it yourself.
Once you have done this, be sure to let us know of any other questions you may have.
Ben