For home:
dips, handstand pushup variants, planche work. Basically a lot of upper body work. If you can't do dips or handstandpushups, mastering a pushup to the deck with elbows by the sides is a must. However, if you cannot do these well, cast to handstand is far off probably. Chair dips and angled pushups at 3/4 handstand or piked on a height handstand pushups.
You can start by holding a pushup position and then leaning forward into the planche and holding for say 5 seconds at a time and progressing to 30 eventually.
Tuck or ball planche.
Building an Olympic Body through Bodyweight Conditioning: A Bodyweight Strength Training article from Dragon Door Publications
Doing a lot of superman rocks or reverse back extensions ( hug a twinkie " reverse leg lifts ) should be done as well. Lay down on something at your stomach so your legs will hang vertically, lift to higher than your butt. You've probably done these before.
Planche walks. Get into a pushup position and lean into the planche until you collapse onto your chest or you can pike your hips like Valentin was talking about to recover ( so you don't faceplant or land on your chest ).