It depends. Some mp3 players are USB mass storage devices. They're not much different from common USB flash thumbdrives and harddisks. It should show up as an extra drive in My Computers as soon as you plug it in. You can usually put files in them by drag and drop. But only the audio files will play.
Others are USB devices, and as such, require drivers. Try to search the manufacturer's website and download one.
And switch on the player before connecting it to the computer.
I just got the Samsung YP-T7 yesterday from an online store and my computer will not recognize the player when I plug it in with the USB cable. The player doesn't even turn on or anything. I am not sure what to do but I think I might be missing DISKDRV.INF I am running on windows XP any thoughts on how to fix this?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic