If your tub is chipped, difficult to keep clean, or just plain ugly, consider refinishing rather than replacing. You'll probably find several companies in the phone book that use various methods. Check samples of their work and read their guarantees carefully. Note that no refinishing method can produce a finish that is as hard and durable as a new tub.
Plan and prepare
If you decide to remove and preserve your old tub, measure it and make sure you will be able to get it past other fixtures and out the door. Remove the sink or the toilet if they will be in the way.
A drop cloth is probably not enough protection for the floor. Cut and tape pieces of plywood to the floor and cover with a drop cloth.
Sometimes old tiles can be removed and reused. However, at least some will probably break. Either find tiles to match or plan to retile the walls. Or install a solid-surface tub surround.
A full day
Screwdriver, strainer wrench, flat pry bar, crowbar, hammer, drill, utility knife, sledgehammer
Basic carpentry skills, dismantling a trap
Locate access to the tub plumbing in the basement or in an adjacent room; if necessary install an access panel.
Plywood and drop cloth to protect the floor
From an access panel behind the tub or from below, disconnect the waste-and-overflow (WO) unit from the drain line. Depending on the installation you may need to unscrew a slip nut or loosen the screws on a no-hub coupling. If the parts are cemented plastic, you'll have to cut through a pipe. Remove the WO unit from the tub. (You may not need to remove the old WO unit if it will fit exactly on the new tub. Measure carefully.)
Remove the tub spout and remove the wall surface all around the tub to a height of about 8 inches. (If there are tub faucet handles, leave them in place if they are at least 8 inches above the tub.) Use a flat pry bar or putty knife to pry off tiles. Cut through drywall with a drywall saw. If the wall is plaster, use a reciprocating saw, taking care not to cut into the studs. Pry off nails or unscrew screws.
Unless the tub is an old-fashioned claw-foot or other type of stand-alone, it will fit fairly tightly between studs on either side. That means you probably can't slide it out unless you cut away the wall surface on both sides. The best way is usually to lift the tub on one end. Pry up one end of the tub first with a crowbar, then with 2x4s. Working with a helper, stand the tub upright.