If you search the forum, people have discussed this issue before (including equipment, supplements, etc). But briefly, you'll need the following (all, please feel to chime in if I'm incorrect or have omitted something):
Pull-up/Chin-up bar (or bands and something to secure the bands with)
Dumbells (or weight bands)
Yoga/Exercise mat (for ab & yoga workouts)
Chair/Stool
Optional:
Push-up stands (I double mine as yoga blocks)
yoga blocks
some kind of recovery drink (would highly recommend)
multi-vitamins (would highly recommend)
Shock-absorbing mat (for plyo exercises)
Protein powder/bars
And you will need to get your kitchen in order. This involves getting rid of all the junk food and stoking every cupboard in you kitchen with tuna cans
This is all I can think of, others will (hopefully) let you know if i missed anything.