I recently got a new computer. I bought this - http://www.easyipodtransfer.com/ipod-to-itunes-transfer to transfer all of my old songs from my ipod onto a new itunes account on my new computer. Then I bought new songs on itunes and I don't know how to transfer them onto my ipod because when I sync my ipod it only comes up with the old songs.

In your devices tab on the left of iTunes should be the iPod you use. Click on that and at the bottom should be some check marks. Check the one that says "Manually manage music and videos". This should make it WAY easier to manage your music the way you want.

Use the iPod transfer to help you.