FlyingZee,welcome to FlyerTalk!
I did last week 2 transits in Delhi, intnl to intnl, no transit visa needed;I'm an EU passport
holder, but I don't think there is any difference for an US passport.
There will be a transfer desk, just follow the signs.
Are you sure about different terminals? I had both my transits (MH-TG) from the same
terminal (T3).