It has always been very basic to always maintain a backup copy of your computer. USe your backup copy ot put everything on your new computer, then sync the iphone.
If for some reason you have failed to maintain a backup, not good, then you can transfer itunes purchases from the ipod to your computer. File>Devices>Transfer Purchases
Create the playlist, and then when the iPhone is connected make sure you click on the Iphone under the left categories. Then click the Music tab, and then select which playlists you want synced. Then you should be good to go after you sync that bear.
If you want to transfer your iPod song to iPhone, try to refer the next tutorial:
Hope that can help you a lot.
No software needed!
You don't need to download any additional software or pay for anything. If the songs are already on your iphone it's pretty simple: I have an ipod nano but am sure it will work on any other ipods.
1. In the top right corner you'll see your devices recognized by your mac. Should say: "2 Devices" in a box by library. Click the "2 Devices" button
2. Click on your ipod. In the top right corner you see an "Add to.." button. Click it.
3. You'll then see a box to the right all you need to do is drag the desired songs to the box and after you are done click "Done."
4. You'll then see your songs in your ipod playlist now! Enjoy!!