I'm assuming you're goal is fat loss? The set/rep scheme isn't going to be all that important. The key is to put some intensity into it and eat right (and in a deficit).
RacerBill has been doing some old school routines in his backyard. Jumping jacks, etc. You do enough of a vigorous exercise and you're going to get your body burning fat. Sure, you might do even better if you had some weights, but you don't.
But, can you get something? One dumbbell? Make a sandbag? Do you access to a chinup bar?
You can do a bodyweight routine like this one, for starters.
Do this 10 times. Record your stop and start times, too.
5
burpees (a whole article on burpees, even)
5 pushups
5
knee tucks (The fifth thing in the video)
5 squats
5 jumping jacks
rest 30 seconds then start the next round
You can keep doing things like this that will kick your butt hard. If you can get a db and/or a sandbag, you can do even better.
CB's TT bodyweight routines have more advanced moves that are harder to do. That will give you the lower rep work, too.