This is a pretty straight forward project. Chances are your unit is attached directly to the studs, with the drywall or greenboard running up to the edge of the fiberglass. You'll need to cut around the perimeter of the shower stall and pull back the drywall that's covering the lip of the fiberglass unit and the nails or screws that's holding it in place. A Rotozip works well for this. Once that's done, pull the nails and the unit should come out in one piece. If not, you may need to get out the saw and take it out in pieces. Wear a mask!
Once it's out, check for water damage. You may need to replace sub-floor depending on what you find.
Your original unit probably developed a crack due to no reinforcement between the fiberglass and subfloor. You'll need to go over the directions from the manufacturer of your new shower unit to determine if you'll need to add reinforcement under the fiberglass or not. A plumber friend I know always sets his shower pans in a bed of mortar regardless.
There's a ton of how to videos out there like this one :
https://www.youtube.com/watch?v=_TEVf4DubtIJust take your time installing the new unit. Make sure you measure
carefully! No one will take a fiberglass shower unit back because you drilled the holes in the wrong spot.
This is a great DIY project. You will probably want to finish off the edges with tile, but that will be dictated by the type of shower unit, the materials, the design of the shower stall and your own taste.
Good luck and post pics when you get it finished!!