In the Battle Frontier, you get awarded Battle Points in each facility after you defeat 7 trainers in a row, except for the Battle Hall, which requires 10 trainers. The base BP received for each facility is 1 for the Battle Hall, 2 for the Battle Arcade, 3 for the Battle Tower, 4 for the Battle Castle, and 5 for the Battle Factory. After particularly long winning streaks, the BP rewarded increases, and you will get the chance to challenge Frontier Brains, who all award 20 BP if you defeat them.
The only other way to get BP is by defeating trainers in the bottom floor of the Trainer House in Viridian City. Each trainer can be battled once per day and give 1 BP for being defeated. New trainers come by communicating with other players via the Pokewalker.