This requires that you are using a device running iOS 4 or greater.

In this example, go into the iPod section of your iPhone and tap on the "Playlists" tab. Note that the location of this tab may differ from phone to phone.

Next, tap on the "Add Playlist..." option...

You will be prompted to name your new playlist. In the example below, the playlist is going to be called "My awesome playlist". You type this in and then tap on the "Save" button...

Every song on your iPod or iPhone will then be listed. Note that songs in iTunes on your Mac or PC, but not on the iPhone or iPod Touch will not be shown. You can then scroll through the list of songs, tapping the "+" symbol to the right of song names to add them to this new playlist.

When you are finished adding songs, tap on the "Done" button. Your new playlist has now been created...