Cotton had Giardia when we first got him. So I'll pass on the advice we were given.
I'd keep kitty away from any other pets you may have, if he's already been around them, they should all be treated for it.Litter box should be scooped and washed/disinfected at least once a day. It's also a good idea to wash/disinfect all food and water bowls and consider washing his bedding and the area around the litter area, just to be safe.
I'm not sure exactly what Cotton (and Freya) were given but it was a single dose pill and the vet re-checked him 2 weeks later. You should start to see an improvement in his stool within a few days after treatment. Cotton was doing better after 24-48 hours, so it's noticeable pretty quickly.
As for handling him - Giardia can be transmitted to humans, but you can still handle him, just make sure to wash after touching the cat and, in the case of kids, make sure they don't touch thier faces or mouths.
As someone else mentioned, Giardia is really easy to get rid of if you don't mind a thorough clean and disinfect regiment. We've had no issues since getting rid of it the first time. Good Luck.