How do I transfer songs I downloaded from iTunes on my phone to iTunes on my computer?

In iTunes under the music tab on your iPhone page there should be an option to synch recently purchased items. Also, iTunes SHOULD be telling you that there are new items on your phone that haven't been synced automatically as soon as you try to sync. I don't know if you changed a setting somewhere because this is default for iTunes.

if it is a mac there is a free software to do it with called Senuti but it is only for macs I believe, but if you are a pc user there is really nothing free as far as programs for that purpose, there is a media player called mediamonkey that you can download and it takes the music off of your ipod for you if you fiddle with it a little bit but some of the names of the songs can be screwed up because of it, but if you are willing to pay a little bit for it you can buy Touchcopy offline to download and it works really well, other than that there is nothing good and free for pc