So if I kill Mr.House and put Yes Man in control it will activate his quest right?

er... I think you have to complete Wild Card: Side Bets

That qualifies as one of the key conditions yes. You still need to bring him to a couple of places.

nah I'm pretty sure if you complete Side Bets and recruit Arcade/already have Arcade you get the quest

Arcade as companion doing Yes Man worked for me, I never took him anywhere, his quest just activated.
I think you only have to do his +rep things if you do one of the other routes.

Where do I have to take him?

South of Nipton is a trigger (a crashed plane) and do the White Wash quest (you get it from Lt. Boyd at McCarren) and help the FotA in the quest.. Also go to The Fort and say something smart (you shouldn't say :'Let's go kill 'em all Arcade!' and also not 'Slavery is the best hope for humanity, buddy!')

Easiest are Repconn and talking to Hildern, the crashed bird can be a difficult area to reach and has high level enemies:

http://fallout.wikia.com/wiki/For_Auld_Lang_Syne#Gaining_Arcade.27s_approval

I've already been to repconn and talk to Hildern before I had arcade as a follower