Note: if you have not done so, please read the introduction to Upgrading a PS3 Hard Drive before performing these steps.
This is fairly simple, just use the navigation in the PS3 to locate the media you would like to backup and copy it to the USB hard drive. The console settings, online IDs and so-forth are retained in the PS3's flash memory, so there is no need to copy this content. Be sure to move any game content, such as game saves and game demos, as well as any other media, such as pictures, video, movies, and trailers.
Once all the content you wish to backup has been moved to the external USB hard drive you can safely remove the USB drive and power down the PS3 console. You are ready to swap the hard drive now. Move on to the next step.