I do this on a regular basis as sometimes I play too long of a game on my PC and need to transfer it to my laptop if I'm traveling.
All of the user files for FM are stored in your C

Documents and Settings\username\My Documents\Sports Interactive folder.
In there you will find your save game, graphics, skins and training, provided you have downloaded or created some.
Copy all of those and place them on a disk, or a flash drive, and paste them onto your new PC. Make sure you have the exact version of FM running on your new PC as the game won't run. So for example if you have FM08 8.0.1 on your old computer, make sure you have that one, the patched version, on your new computer. Seems silly, but I've seen others asking the same question and their problem is just that, they forget to install the patch they were using.
Hope that clears it up a bit.