How do you change oil on a mercury 60 hp two-stroke outboard?

Engine oil

You don't change this - just keep adding more (either with the fuel, or in the oil reservoir if the engine has oil injection)

Gearbox oil

There are two screws on the side of the gearbox (at the bottom of the leg). Take both of them out to let the old oil drain out (try to control where it goes - it smells disgusting).

Check that the old oil hasn't gone milky. If it has, you've lost a seal and water is getting into the gearbox (get this fixed - ignoring it will rapidly prove expensive)

Inject fresh oil into bottom hole (you can buy a pump to do this, or get your oil in a squeezy tube with the right size of nozzle) until it starts to overflow out the top hole. Replace the top hole plug to airlock the oil in, before removing the nozzle and plugging the filling hole.