the difficult part is the drain. on the tub it is at one end. shower stalls usually have one in the center. the drain can be moved unless you are on a cement slab. then there is a way to build your own shower base. the most common way is to use tile... use floor tile because wall tile is slippery.
You would also have to retile the whole thing. You can tile it yourself. I read a book on tiling I picked up at Half Price books and redid my entry way just from the knowledge from that book. Turned out really nice too.
It depends on you and the type of tub and if you have tile walls.You might be able to remove all and just slide in a new shower unit but dont count on it. You well have to redo your water lines and may have to build a base for the shower base unit to sit on for the drain again it depends on where the old tub is sitting and if you are on a slab or wood floor. Second floor, first floor.
First time diy I would get help from a friend who has done this type of job before. You might get a plumber to do the pipes and you do the rest.
I know where you are coming from the price to have this work done would not be cheap but unless you have done this kind of work before I would take a step back and give it some thought.
There are many variables when changing a tub to a shower. For one in many municipalities a tub drain is 1.5" in diameter and a shower is required to have 2" diameter drain. Also others mentioned moving the drain to the middle. Also there is proper construction of the shower. And tearing out the old tile. Go over to John Bridge Forum and us tile pros can walk you step by step through the processes of a properly constructed shower.