I've never really had to think about it - I just do it, but I guess that I rest the tiller on my aftmost shoulder when I'm out on the wire if I have to use both hands. Virtually all the time I'm able to sheet block to block one-handed (pass the first pull to my tiller hand, second pull is all with my forward hand).

If I'm sat on the side I'll just let go the tiller if I need to use two hands.

As for getting out on the trapeze, I don't use a hand - I just clip on and push out.