moo,
Firstly you need a clearance to go off track... it's usually available unless there is converging traffic. ATC will ask you you to report back on track, or be on track by a certain point (they generally like you on track by an FIR boundry to complify coordination - but thats not always achievable).
Then you leave the FMC and fly headings around the weather. It would be unwise to disengage the autopilot, as conditions around a storm can significantly reduce the performance of the aircraft.
The turns aren't usually large, as you've started generally them 60 odd miles away from the storm. Things can get a lot busier if a clearance takes a while, or if the storm is in the way of terminal maneovering...
Lancer