Bicycle Mechanics - newbie alert...bottom bracket installing help

If I install a sealed cartridge bottom bracket do I have to use both cups? I mean can I use the existing non drive side cup and just install the new one. I hope so because that would make my life so much easier. I fear the other cup is stuck.

You want to use the left cup that comes with your new bottom bracket. Even if they are identical models and sizes, the chances are that it won't go back in to exactly the same spot and you will end up with creaking or you won't be able to tighten down the drive side enough. There are tools to help remove a stuck cup and sometimes this is easier with the BB in the frame (to use the axle to help hold the tools in place). Good penetrating oil and patience is what you want to start with. And remember to grease the new one (or some form or appropriate liquid for your frame type).

You do realize driveside unscrews clockwise, non-driveside counter clockwise?

You could probably get away with it, but I find that most times you have to screw in the cups a little on each side at a time instead of all the way in on the driveside.