You can't download any wallpapers directly off the internet from the phone itself unfourtunatly. What you should do is make a folder in your Pictures folder on your computer and save all the wallpapers from whatever site in that folder. I have a general folder for my iPhone stuff and sub folders in there because of the mass amount of wallpapers i've pulled off the internet.
When in iTunes with the iPhone connected, go to the Pictures tab listed in the iPhone menu. Click on the top of the drop down to select what folder it will upload your pictures from. Find the folder you have just made and select that. Then check off whatever sub folders you have created and want to add those pictures to your phone. Then on the bottom right click apply, and it should Sync the iPhone and Optimize and transfer yor pictures. Hope I helped you out. Any other questions PM me, and Welcome to the iCafe!