Thanks for the advice. I am planning on taking the tiling class at my local Home Depot on Saturday. Hopefully, I will get some useful tips.
Since I only want to regrout the shower floor, where do I stop in removing the old grout? I don't want to mess up the grout in the corners that connect to the wall tile/grout. How do I handle the transition from floor to wall? And how do I handle the grout around the floor drain? I certainly don't want to end up with a bigger problem than I already have!
Was this crack at a joint where the wall meets a wall? or where a wall meets the floor? Those joints should be sealed with a non latex caulk as latex will certainly mold in a shower. If latex and/or siliconized latex is used, then you're looking at mold and replacing the caulk every few months or years. If you use 100% silicone, then you can not worry about it for decades. Silicone is also mold free.