Move any MP3 files that aren't in your music folder ("Music" or "My Music") into the music folder. The window in which you can view the contents of the folder is called an Explorer window (in Windows) or a Finder window (in OS X).
Scroll through the folder and decide on your organization method. You might choose to make folders by artist, perhaps with subfolders for album, or by genre, or by some other method that makes sense to you. No choice is set in stone, though reorganizing might be tedious depending on the size of your collection.
Right-click in any empty space in the panel that displays your MP3 files. Select "New" then "Folder" (Windows) or "New Folder" (Mac).
Select the folder and press F2 (Windows) or Enter (Mac), then rename it. Name the folder according to the method you selected.
Click on the first title that belongs in that first folder and drag it into the folder, then release the mouse button. To move several titles at a time hold down the Ctrl (Windows) or Command (Mac) button and click each MP3 file you want to move. When they're all selected, drag them into the new folder.
Continue making new folders and moving songs into them until either all the songs have been organized or you have several songs remaining that you can't categorize. After all, it's inefficient to have folders meant to hold only one file apiece. The remainder you might leave in the root music folder or place in a new folder called something like "Organize Later," "Miscellanea" or "Everything Else."