Inspect the walls that will be covered with the surround for any loose paint or plaster. Remove all loose material with a drywall knife. Remove any chunks of plaster that are not firmly attached but do not remove plaster that is solid. Fill in any cracks with drywall compound. Tape any large openings before attempting to fill them. Allow the drywall compound to dry overnight before continuing.
Check the floor where the tub will sit for soundness. If this is the same location as the old tub and it is level, you should be able to install the new tub right on top of the old site. Repair or replace any damaged lumber before proceeding. Refer to your new tub's installation manual for specific installation requirements.
Fit the tub into the prepared space. Check for level and use shims if necessary. Shim the tub tightly into the space so that it cannot move. Attach the existing drain and overflow to the tub. Pre-cut holes into the front wall of the surround just large enough to accommodate the existing plumbing. Measure carefully or create a template with a piece of cardboard as there is no way to undo a poor cut in a tub surround.
Refer to the tub's installation instructions for the recommended method of installing the panels -- many have pins or flanges that fit in a precise order to complete the installation and may or may not clamp to the tub or each other.
Adhere sections of paneling to the wall and to other parts of the tub kit with construction adhesive. Begin with the largest section and work outward. Glue each panel before moving it into the tub area with a bead that begins in one corner and undulates across the panel to the opposite corner. Press the glue bead tightly against the wall and hold the panel in place until the bead becomes tacky. Attach a nail-up wall system by pre-drilling through the surround lip and into the lath. Complete the installation with screws; never use nails on old plaster.
Reattach the faucet and shower head to the plumbing stubs that protrude from the front wall of the tub surround. Caulk the seams between the walls and tub, as well as the seams where the panels join. Caulk the trim at the tub's joint with the floor. Allow the caulk to dry for 24 hours before using your new tub.