To replace your rear coaster brake wheel with a multicog wheel, you will need: Rear wheel with six speed freewheel, axle mounted derailleur, rear BMX caliper brake with lever and cable, shift lever and a longer chain. It may be cheaper to buy an old mountain bike from a yard sale and get the parts you need from it. If all the parts come from one bike, you know they will work together.
Sturmey Archer, Shimano and SRAM make internally geared rear wheels (similar to the old three speeds, but with up to nine speeds now). They are very cool, but cost four or five times as much as a derailleur gear setup. You can get the internally geared hubs with coaster brakes, drum brakes and sometimes disk brakes.
