What are the best steps for removing an old tub/surround and putting in a new one?

First, turn off the water going to the bathroom. Old tub if porcelain, ceramic, disconnect the drain and faucets, etc... Lay down cardboard and plastic on the floor. Grab safety goggles and start smashing! Use a sledgehammer and you will get it out in no time. Then, when it is cleared, check the floor for rot decay etc... you will need to repair that first. Check the floor and make sure it is level and the walls are plumb. If all is ok you can install, I am assuming here a new tub + surround. If it is all in one, make sure it will fit through your doors and into place. They are usually used in new construction and put in before doors and frames. You can buy a tub and then a surround for the top made of fiberglass inexpensively. If your walls are square it is relatively easy, otherwise you will have to build out or cut back into the walls to square it up. You set the tub in connect it to the drain. Keep the drain filled with a rag so you don't get any material in there while you measure, mark, and cut holes for the faucet and shower head to slip through. Some additional plumbing my be necessary. You will use silicone or other water resistant caulk to fasten to the tub and surround. The tub will have its own fastening issues. If you use a clear caulk for the joints and corners you won't see it as much or you can use white to match other caulk in the room. It takes a weekend to do this even if you don't have to sweat pipes or re plumb the walls. Good luck!

If it's a plastic or fiberglass tub surround, you can cut it out with a saw. Either a circular saw or a reciprocating saw will work but you will have to be very careful to not cut framing members, wires and pipes. Very careful.

If it is a porcelin-over-steel tub, it's going to take a lot of muscle. Clear the wall surround away from the top edge of the tub, then make sure that all screws and nails securing the tub are removed. Disconnect the drain and just use your muscles and a crowbar to pry the thing out of there. In my experience it can be done but it's hard work.

Good luck!

Hire a professional if you don't know what you're doing.

They had to cut my old tub into pieces because it wouldn't fit through the door. Then they had to buy a retro-fit remodeller new one for the same reason.

Make sure it's leveled properly and blue backer board used behind it. Add access panels for the faucet connections if able.

Warm Rain is a good brand, in my opinion.