If you haven't got iTunes installed on your computer then you can download it from here : http://www.apple.com/itunes/download/
You can then sign into your account via the Store drop-down menu at the top of it (you may need to press alt-S for the menu to appear) - I appear to have cropped the below screenshot, but as well as those options that are shown below there should be a Sign In option :
If you have already bought items on your phone and you haven't yet synced it to a computer then this article might be of help : https://discussions.apple.com/docs/DOC-3141
With iTunes 11 you can enable the left-hand sidebar in iTunes via control-S, which might make some things easier. To sync content to your iPhone you then connect the iPhone to your computer, select it on the left-hand sidebar, and then use the tabs on the right-hand side to select which of your iTunes content to sync to it.
Syncing music : http://support.apple.com/kb/HT1351
Syncing apps : http://support.apple.com/kb/HT1977
Syncing photos : http://support.apple.com/kb/HT4236
Note that ringtones (and audiobooks) are currently a one-time only download, so you may want to take backup copies of any that you buy. Music, films and tv shows can be re-downloaded in some countries, but there is no guarantee that they will remain in the store for future re-downloading, so again you should take your own backup copies of them. If you purchase any items directly on your phone then you should be able to copy them over to your computer via File > Transfer Purchases (alt-F to open the File drop-down menu, and File > Devices > Transfer Purchases on iTunes 11)