Trimming up the edges
Most of the time, the neckline in the back and the sideburns will require special attention. For some reason, the clippers like to ignore that neckline hair and leave it long.
Look in the mirror as you do the next part. (I'm not looking in a mirror in the pic, only because I'm facing so the camera can "see" the scissors well. Ordinarily I would have my eyes planted on my reflection at this point!) Look for long hairs sticking down in back, that you can see from the front. That is, the area of the sides, of the rear hairline behind the ears. Usually you'll see a fairly long patch on each side, hanging down behind the ears.
Carefully trim off that long thing from each side. GO SLOW, and feel around as you do it (don't cut your fingers though!), to make sure you're only getting the hanging-down part and NOT cutting into the "main" part of your hair!
As for the part you can't see at all, I personally ignore it most of the time, since with scissors, it's too easy to cut an unwanted groove into the unseeable parts. Grooves in black hair that's been cut short are unhideable, so it's better to have a bit of extra hair left in the far back, than a groove that'll be glaring out for 2 weeks until the hair grows back. Don't go by the feeling of hairs laying on your neck at this point, since that's usually just from all the hairs that have fallen back there since you started trimming!
The next part is the sideburns. Cutting them short is simple in principle, but not-so-easy for a beginner! Trim cautiously for the first few cuts, and leave a bit of extra hair so if you don't get them precisely even, it won't bang out.
The principle itself, like I said, is easy: Just trim off any too-long hairs hanging down. Take care not to cut a groove (where it's accidentally cut off at the scalp) in partway up the sideburn. There is no real way to hide a groove with short black hair.
Now, comb your hair, front-to-back, before using the scissors anywhere else.
Once it's combed, take note of any stubborn bumps that are still showing. Just combing it will get rid of most of the bumps. The combing separates the strands, and also helps to get them all aiming in the same direction again.
WARNING: This is the touchy part:
If any obvious bumps are left, carefully cut them to the length of the rest of the hair with the scissors. Try not to turn a bump into a dip! If you do end up with a dip, don't try shortening the surrounding hair to match! With so little hair left, you can end up with an unhidable patch if you do. So just ignore any dips. You can "play with" the surrounding hair with your fingers, a comb, or a pick to help hide little dips.
Now it's time to prepare the trimmer for storage.
First, remove the comb from the trimmer. Then, clean out all the hair clippings from the blades and surrounding areas. The Wahl kit comes with a little brush for this, but if it gets lost, a nail brush will work fine. It's almost impossible to get all the clippings totally off the clipper, but they should definitely be removed from the teeth of the blades. Don't bother to take the blade assembly apart or anything, just brush it off. The reason for doing this is to keep the blades from rusting, and to keep from getting a nasty mess going. Old hairs and old clipper oil turn into a yucky gelled mass if left alone, so best to get rid of that stuff before it's old! Also brush the hairs off the clipper combs.
Now that the blades are free of hairs, put a new layer of oil on (just like when you started cutting your hair). This will keep the blades from collecting the invisible moisture in the air and rusting. Surprisingly, the oil will most likely evaporate before you cut your hair again (figuring about a month between cuts), but enough of a film will remain to protect the blades from rust.
Put the clipper and combs away.
Now that all of the actual cutting and clipper storage prep is done, it's time for the final combout!