What do I do with geraniums once they have finished flowering?
Geraniums or pelargoniums?
Depending on how tatty they look and how early they finish flowering you can either:-
Cut them back to the ground and give them a feed and water. They'll grow back in about 3 weeks time and flower again as long as it's done by mid August. Later than that you'll probably just get new foliage.
You can simply trim off the finished flower stems and just pull out the exhausted foliage from round the edges of the plant leaving newer foliage which, if they're like mine, should already be growing from the middle.