At the Yiga Clan Hideout, you learn that new recruits join by visiting the three clan branches and obtaining the Yiga Clan attire.
Quest Location
To start the quest, talk to Mimos at -3686, -1366, 0331, which is east of Gerudo Highlands Skyview Tower and west of the Yiga Clan Hideout Chasm near Rotsumamu Shrine. You can't enter the hideout from the door that faces the chasm. The front door is to the west of that, on the other side of the cliff.
How to Complete the Quest
Mimos mentions a rumor that the Yiga clan took over the ancient tech lab in Akkala. You can get there by going northeast from East Akkala Stable. Check on the door and you will have to battle a Yiga enemy. Inside, you can talk to the tailor to receive the Yiga Armor. There is also a map on the wall that shows the location of the other Yiga clan branches.
There is a Yiga Clan hideout on the Great Plateau, which is south of the Hyrule Field Skyview Tower. The hideout is south of the Temple of Time ruins on the Great Plateau. Check on the door there and defeat the enemies, then talk to the tailor inside to get the Yiga Mask.
This is another hideout at the Yiga Clan Maritta Branch, where you can get the Yiga Tights.
Equip the full set of Yiga Clan attire, then check on the door of the Yiga Clan Hideout, and they will let you in.