App Store Apps
The easiest way to do things is to get an app from the App Store. Before jailbreaking my phone, I used an app called Folders Pro.
Folders Pro ($2.99, Apple App Store) is a neat app that lets you move files back and forth from a special area created by the app on your phone. It's pretty easy to use, however you can't transfer files with a USB cable, meaning you can only transfer via WiFi. This could mean slow transfers if you're trying to copy many large files. The files are also stored in the app's data, which means that if you delete the Folders Pro app, you've lost all the files you put on your phone.
Air Sharing ($2.99, Apple App Store) seems to be basically the same thing, only a little more pricey. It seems to be a solid program, but I have not used it personally.
Folders Pro worked exactly like it said it would, but I felt it wasn't the best solution for me. If you don't want to jailbreak your iPhone though, it's a solid choice.