How to replace a bath tub
Honestly, It can be a giant pain in the butt.  

You start with covering it with a thick blanket or two and smashing it with a sledgehammer to bust it up into pieces (yeah, that's really how it's done).  The blanket is to prevent getting yourself cut up by flying pieces of cast iron and porcelain.  You might also have to bust out the tile/brickwork as well, depending on how things fit together.

To get the new tub in, you might just be able to get it in the door, but many bathroom doors in older houses are of the 24" variety and you can't fit a tub through them - especially if it's a one piece shower/tub system.  If that's the case you will probably need to take the door out, cut out a stud on one side and bust up the wall a bit to get the new unit in.  Then of course rebuild it all once you got the new tub in.

I would strongly consider re-glazing your existing tub.  It can really make a crappy old tub look like brand new.