Step 1; Open Itunes
Step 2; Create new playlist with the + button at the bottom left(?) of your screen
Step 3; Choose your songs & drag and drop them over your playlist
Step 4; Check playlist to make sure it has everything you put on there in it, if not then add it again.
Step 5; Connect your Ipod via USB or the Firewire cable
Step 6; Your ipod should show on your itunes (If you have trouble with this and have more than one USB cable or USB slot, try all options, my Ipod only works with one of the 5 slots i have...). If you have already set it to sync with your playlist, it should start to sync by itself, you can stop this but tbh it's best to let it do it's thing.
Step 7; Go onto your 'ipod'. Check it's fully updated, and then go into the music tab.
Step 8; On this tab you will see the list of playlists available to add, make sure a tick is in the box of any you want syncing onto your ipod.
Step 9; Click Apply at the bottom right corner
Step 10; Click the Eject button, and enjoy your music :)
If this doesn't work then set your ipod back to factory settings (this will delete everything already on it) and try the steps again on a clean slate.
Hopefully this helps?