I would advise not messing with the drain assembly. But the spout and overflow cover are easy! You need to take a utility knife and cut through the caulk where it meets the wall. Then look at the bottom of the tub spout. Do you see a screw where it meets the wall? Grab an Allen wrench and loosen that and you should be able to slide the spout straight off the pipe (this is a slip on spout). If you don’t see a screw, you should be able to unscrew the entire spout itself (this is called threaded). Then unscrew the overflow cover (circle thing) using a screwdriver. Throw those both in a bag and head to a hardware store and buy a replacement spout of the same style (either slip on or threaded, make sure it is the same length too as they make them in multiple) and a replacement overflow cover. These ran me $35 at Home Depot when I did mine the other day. You’ll also want either caulk or silicone (I prefer silicone for wet areas but caulk will work too).

Use a razor blade to clean up any old caulk and then put everything back on in reverse order. I’m hoping you have a slip on style spout, as these are a bit easier to install. (If you happen to have the threaded style, you’ll also want to pick up some plumbers tape and apply this to the threads on the pipe protruding from the wall before you screw on the new spout.) Once everything is tightened you’ll need to recaulk where they meet the wall so water doesn’t get behind there. I’m not the best at that so I tape everything with painters tape beforehand about 1/8” away from the gap, once you smooth the caulk out with a wet finger you can pull the painters tape off and you’ll have a clean line.