Most strops when new will need little to nothing done to them. If they happen to be a bit bent (due to shipping) put it on a flat surface (like a table) and put a heavy book or two on the strop to flatten it out.
Periodically apply some strop dressing (like the product on the right) to your strop to keep it supple and hydrated. Some prefer neatsfoot oil, and various other products, and some strops (like Tony Millers) will often come with either a blend of oils he uses, or a dressing similar to the one on the right (Fromm #364). Different products are applied in different manners, but if it is a strop specific product it will tell you how to apply it, as does the example below.
If you happen to nick your strop, provided it isn't a big gash, relax! You can still effectively use your strop. Each case is a little different, but typically you merely need to remove the loose piece so it isn't flopping around. Sometimes it may be necessary to use some VERY fine grit sandpaper to polish up the area to make sure it is smooth and below the main level of the hone, as if the nick is below where the razors spine/edge touch, you shouldn't have a problem.
Provided you are reasonably careful with your strop, and take good care of it, it should last a lifetime!