There are 16 spirits you can get in the game. they are found mainly in the northen part of the island. to get them you need to find them, like any other duelist, and beat them in a duel. it is random if they will join you or not, so it might take a few attempts to get them. Here is a list of when they are unlocked:

Code - Effect

Acrobat Monkey - Defeat Kagemaru
Adhesive Explosive - Starter at well
Babycerasaurus - After finalists are decided in tournament
Batteryman C - Finish game
Batteryman D - Finish game
Beelze Frog - After finalists are decided in tournament
Blast Asmodian - After finalists are decided in tournament
Dragon Capture - Jar Finish game
Ebon Magician Curran - After Abandomed dorm events
Hane-Hane - Defeat Bastion for the second time
Jerry Beans Man - Starter at well
Oscillo Hero #2 - Starter at well
Skelengel - Defeat Kagemaru
Soitsu - After Abandomed dorm events
Star Boy - Defeat Bastion for the second time
White Magician Pikeru - Finish game