Summarize this article:

The first step is to shut off the water for the bathroom you’ll be working in. Locate the main line and turn it all the way off. Then, turn on the faucet in your tub to drain the lines. Use a screwdriver to unscrew the faucet and disconnect it from the water lines by unscrewing it. Remove the handles, overflow drain cover, and the drain cover on the bottom of the tub. If you have a showerhead, remove that as well.  You may need to pry off a plastic cover to gain access to the screws. You may be able to reuse some of these accessories, so keep them if you don’t want to buy new ones. You need to expose the studs in the wall in order to install a new bathtub, so you must remove the existing surround and the drywall behind it. Using a utility knife, cut through the drywall around the outside edge of the entire surround. Then, use a pry bar to pry the drywall and surround or tiles out of place. Be careful not to damage any pipes or wires!  Be sure to wear safety gear, including goggles and a dust mask, throughout this process. Work from the top of the surround down to the bottom. In some homes, you may be able to access the plumbing from the room next to the bathroom. In other cases, the plumbing may be situated in the floor under the tub. Most likely, you'll need to cut a hole in the wall or floor in order to access the plumbing. First, unscrew the tub drain and overflow from the P-trap underneath the tub. If your tub is acrylic or fiberglass, cut it into pieces with a jigsaw to make the removal process easier. If you want to try to keep the tub in one piece, use a jigsaw to cut away the tub flange that’s nailed to the studs, then tip up the tub and pull it out. You may need to slice through the caulk that connects the tub and floor before removing the tub. Use a utility knife to do so.

Summary:
Turn off the water at the main line. Remove the accessories and disconnect the water lines. Remove the existing tub surround or tiles. Gain access to the plumbing. Take out the old tub.