Demolition doesn't take much skill, just a lot of work and an ability to put up with messy, dusty conditions.
Remember to shut off water pipes and disconnect wiring before cutting into the walls and floor.
Stuff an old rag into any drains you expose during the tear-out. That'll keep harmful sewer gases out and prevent construction debris from falling in and plugging the line.
After turning off the water, flush the toilet to empty the tank. Soak up any remaining water with a sponge.
Have a bucket on hand to catch excess water and disconnect the water supply line to the tank.
If the toilet is two-piece, unscrew the two nuts under the tank and remove it. Unscrew the two closet flange nuts/bolts anchoring the toilet to the floor.
Firmly rock the toilet back and forth or carefully pry it up from the bottom to break the wax ring seal.
Lift the toilet bowl off the flange and stuff a rag in the drain to prevent sewer gases from entering.
NOTE: In some states it's against the law to resell a used toilet, so if you don't have another place for it, dispose of it properly.
Disassembling Vanity Sinks
Under the sink, undo the compression fittings connecting the trap to the sink's tailpipe and drain pipe.
As you remove the trap, catch excess water in a bucket, then stuff a rag in the drain to block gases.
After turning off both water supplies, detach the hot and cold water lines running to the shut-off valves.
You may be able to remove the sink and faucet together, but if necessary, remove
the faucet by unscrewing each nut under the valves from below.
Pry up on the lip of a self-rimming sink to break the caulk seal holding it to the countertop. Or, if the sink is an "undercounter" model, undo the clips holding it on the bottom.