Q: how do i restore a deleted picture from iphone

If you've previously synced the pictures to a computer (as is generally advised to archive them), then they are gone, unless you have backed up the device to itunes or icloud.  If so, you need to perform a restore:

http://support.apple.com/kb/HT1766?viewlocale=en_US&locale=en_US

Go to Settings>General>Reset and tap Erase All Content and Settings.  This will erase your phone.  Then you will go through the setup screens again as you did when your phone is new, and when given the option, select Restore from iCloud Backup.

Note that you cannot restore just one file, it's all or nothing.

If you didn't back them up, and you didn't upload them to PhotoStream or some other online photo repository, you don't. They are gone.