Based from what I did with my friends and what I found on the net... (actually what we did was trial and error. We tried stuff, then checked if it works. If it didn't we'd try something else. It took a while though.)
1 - authorize your computer. It's under the STORE tab/menu (you'll need your apple Id for this)
2 - (if your device isn't connected yet, connect it now.) I'm assuming that your phone is synced with your previous laptop, so itunes will ask something about 'erasing and syncing' and 'transferring purchases'. Click on 'Transfer purchases'.
**If there's no prompt or something like that, go under the FILE menu, then under DEVICES, choose 'transfer purchases'
[actually I'm checking on itunes now, just to make sure. haha]
And... I think it's done!!
Additional stuff:
I once transferred songs from my pc >> phone, and used this program called iTools. Just in case the steps on top don't work, try it. There are lots of guides on doing it on youtube. Give 'em a shot and good luck!!