I shave my armpits, (mach 3, borrowed from Mr Smith--he now doesn't want it back) and get a professional in for if I'm going to be swimming.
I might shave my legs in the summer for aero benefits but they're not very hairy, so I don't usually bother.
Mr Smith shaves his head, and sometimes his chin.
As to how to do it, slather area in lather (soap is sufficient for arm pits, foam is better for larger areas) and stroke away with razor. Follow the grain, ideally.
If you get a pro in, lie back and think of England. They'll tell you what you need to do. Waxing is neater, lasts longer, and doesn't give such irritating stubble on regrowth.
Moisturise well afterwards whatever method you use.
Generally, I resent the societal expectation that one's limbs and areas should be doll-like hair free, but it can actually improve undercarriage issues on long rides. Hair holds scents and fluid sticks to it. Sometimes it's better without.