Experience is earned in Yakuza 6 by playing mini-games, fighting, eating or progressing sub-stories and the main story. You basically earn it practically doing any activity in the game.
There are some ways to increase your exp gain. The "Yakuza Gear" increases your exp by 30% but needs to be offset by a stamina increasing equipment. It can be acquired from the second Ono-michi mascot sub-story in Onimichi. Easier methods are skills that increase the exp gain for a relative exp type. These require investment into the health and defence stats to unlock. Another method are drinks from vending machines but they only affect a limited number of battles.
Regardless with what you do, 100,000 exp is not a lot and should be acquired before beating the main story. You will need a lot more than that to max out Kiryu though.