Lets build it from the bottom up! Starting with your reservoir make sure that it will be dark inside, since I used a fish tank I covered it in cardboard and duct tape, you should be smart and get a reservoir that doesn't need anything done to it. In the reservoir place your air stone, connect some tubing and hook it up to your air pump. Only advice there is place the air stone at the opposite end of your pump or at least not next to the pump intake. Next place your sub pump in the tank. Bang your reservoir is basically done, only thing to do is connect some rubber hose to the pump to get the water up!
So lets move up to the grow tray, in the grow tray you are going to need 2 holes, one hole is for the hose from the pump the other is your over flow. Lets start with the over flow.
I recommend placing the over flow anywhere except where you think you might be planting, in my case I wish I had placed it either smack dab in the middle of my grow tray or more off in a corner. Being a newbie I rushed and placed it way too close to a grow pot. Basically this pipe need to be big enough to allow the water to go back in the reservoir as fast as your pump bring it up to the grow tray. The over flow also sets your water level in the grow tray since all water reaching that height goes into it and heads straight back to the reservoir.
So what to do Cut a hole in the plastic bin just big enough to friction fit the overflow pipe into it. Once you have placed it in such a position that the bin won't overflow and your mesh pots will be covered approximately half way up then silicone it in place.
Next you need a hole to act as the fill hole and main drain, place this in a corner and slightly tilt the whole thing towards that corner for easy draining when the pump is turned off. There are many ways you can do this but the cheapest way I came across was to cut a hole the size of a 1/2 grommet. So we cut the hole place a rubber grommet into the hole, now we have a nice looking hole with a rubber grommet. In this hole we need to put our fitting that connects to the rubber hose / pump. I recommend putting some silicone around the grommet, fitting, and rubber hose to prevent any leaks once you have them together.
Basically that is it, some how get the grow tray above your reservoir which is where the sturdy materials I talked about earlier come in. If I had a big area mine would be sitting on a sweet table that also acted as the grow tray. Not sure where you plan to have it sit but as long as one is over the other the system works. Mine is basically a plastic storage bin resting on top of aluminum crutches that allows it to rest on the fish tank.
I have included some pictures below to illustrate what I can. Sorry my system is really small so not the best for picturing to describe the setup like a big one would be.
First picture is of the overflow pipe (grey one) next to the fill / drain hole in the corner.
Second picture is of the drain hole basically just a grommet and silicon.
Third picture is weird, you can see the side of the grow tray, the crutches I used to support the tray sitting on the reservoir, some garbage bags to cover up reservoir, and aeration taking place in the reservoir.
Hopefully this helps a bit, remember this is just a tiny system and could easily be much bigger with very little price difference just get a bigger reservoir and either a larger grow tray or even multiple grow trays there are lots of possibilities. Good luck