Walked around on foot at first and getting on, walk around until they start to loose attention to their surroundings before you pick up speed. Keep their attention on you, that way it prevents as much spooking
For me personally the hardest part was getting him used to the echoing sounds. We had a good couple of spooks from footing hitting the walls lol.
The environment can change a lot the horse's behavior (it's closed, usually grounded and near to the public). If you can go to an indoor arena before the competition, that would be great! If not, try to go to smaller competition than you're get used, at least at the first times :)
You have 2 things about the indoors: the first, jumps are coming faster (there's less space). You can work on this, with jumps just before a curve, shorter lines and most important: it has to turn a lot!