He is just running his guitar through a multieffects pedal. In his case the zoom G2, which is a relatively inexpensive choice. No idea what effects he's using. But if you want that type of sound, you'll need a uke with a pickup, and either a combo amp with some cool effects, like in the Vox DA line, or an amp and a multieffects pedal.
Vox DA5 FTW. Only thing that could make it better would be more power...but I'm not quite ready to put down that kind of money.