All right, I'll use your skimmer pic as a reference. The down-tube on the left descends from the catch cup. You'll want to hang it over the side of your sump down into some sort of a catch basin. It'll start to collect stinky amines and other organic compounds. You'll want to clean your catch basin regularly.
The middle down tube, with the small clear air line entering it at a 90° angle, is your inlet. You'll need to feed water into the skimmer here. The little air line will actually suck air into it, as water enters the inlet, thus making your bubbles and subsequent foam. Your foolproof bet is to use your smaller submersible pump to supply water to the inlet. You'll put your smaller submersible pump into the same baffle chamber as the skimmer in this case. Whatever the case, at some time in the future, you'll probably want to buy a bona fide magnetic drive-coupled pump to handle all your water pumping tasks.
The flexible hose with the little red top is your water outlet. Skimmed (foam fractioned) water will exit your skimmer here. The little red breather is to keep it from gurgling. If it wasn't there, after a while that would drive you crazy, and you'd start to imagine all sorts of far fetched things, like Denver in another Super Bowl for instance. :thinking:
As an experiment, hook the skimmer's water inlet to your sink faucet or garden hose. Turn on a little water (not too much!) and watch how it works. Once you see it going it'll be a lot easier to understand what it does.
You can use the output of the skimmer to leak water over your bio-balls if you wish, there are a few schools of thought on this idea. I'll let someone else elaborate.
You'll want your large submersible pump to return water back up the tank sump (I'm assuming the returns have a pass through design), and back into the tank by way of one of the two white plastic return pipes. Like I mentioned earlier, you will eventually want a more powerful pump to handle your pumping tasks. That way you can make use of both of your return tubes.
I'm sure this will generate a few more questions, so fire away.