Can someone help me transfer downloaded music to my granddaughter's MP3 player?

What brand & model of player is it? Different players have different techniques. Some you can just copy & paste into the mp3 icon on the desktop when it's connected to the computer. Some, you need an intermediate program which acts as a media manager. See if the player came with instructions & also see if it came with a cd. If there's a cd, then that might have the Media Manager program on it.

Not all players come with instructions or very good ones. So if you can tell us the brand & model ...

It is a SanDisk M230. It shows to use Windows Media Player to transfer music. I just don't know how to download with LimeWire to Windows Media Player.

Go to your LW Library window, select Saved Files folder & press the Explore button. Sample image here: Using Library Explore button to access downld folder (click on link) & the folder will open up for you. That's where your downlds are. So you can right-click & open with ...wmp, OR move them to your Music folder before adding to WMP.

Normally the default location is C:\Documents and Settings\"your account name"\Shared

YOU ARE THE BEST!
Thanks so much!