Having a cracked, leaky, ugly and old bathtub may egg you on to consider replacing it. Upgradation for better features is a good cause too. However, a lot of good can come from sealing the cracks with putty or hydraulic cement and just re-glazing the tub. This can save a lot of time and effort.
Before you begin to work on dismantling your old bathtub, warn a few friends that you will need them to help you move your bathtubs. Bath tub DIY can be awfully heavy for one person to deal with. You'll be saved half the trouble if you just fitting a new one in a newly built house.
You could work with your old plumbing for a new bath tub DIY fitting. You will need among the other common fittings a P-trap, a PVC drainpipe and an overflow pipe. Tools you will find handy are a pipe wrench, a hammer, a drill and a hacksaw. You could also use a level, plastic shims and measuring tape.
Do measure the area that the tub should go into before you pick up a new tub. The last thing you want is to spend hours looking for the perfect tub just to find that it doesn't fit. Also, if the new tub allows for some extra fittings, make sure you've bought the plumbing fixtures you'll need to modify your plumbing to suit the new tub.
To remove the old tub you will have to break the caulking around it, which attaches it to the floor and the walls. Caulking is also what waterproofs most tubs. To get the tub out of the room, you may have to break a wall if it won’t fit through the door of the bathroom and even dismantle the faucets. Before dismantling the faucets, you have to turn off the valve that brings water to it.
Before placing the new tub, make sure you've cleared the floor of caulking and put together a new mortar bed. Level the tub using plastic shims as plastic doesn't rot like wood and leveling should be done such that the ledger board, the lip of the tub and the wall studs are aligned for proper nailing of the tub. Before nailing however, the drainpipe should be shortened/lengthened according to the height of the tub and the trap should also be fitted.
Also ensure the overflow opening is attached to the drain plug assembly and that the cover plate for the overflow is in place. Fitting the plumbing and the faucets to the tub and make sure everything is ok. Then waterproof and seal your tub using caulking or waterproofing sealant. It is recommended, the latter because unlike caulking, it is elastic and does not crack because of temperature fluctuation in time.
If you need to join a galvanized steel pipe to a copper pipe, use a dielectric/brass fitting in between. Also use plumbers' putty or Teflon tape to seal threaded joints. Not doing these simple things can cause massive corrosion in the former case and a leak in both.