I'm more than a bit jealous of Technologygarden's website. Mine looks like poo compared to his. I just don't really have the time to figure out how to make mine look nicer (I'm kind of hammering the square peg in the round hole just figuring out how to make stuff show up on mine.)
tolledot - what kind of hydroponics you'd want to build depends a bit on what you want to grow. If you want to grow some leafy greens (spinach, lettuce, etc) a great way to do that is with deep water culture (DWC). You can look at the blog on my website (linked below) and see how I built mine.
I've modified it a bit, as you can see over the course of my blog entries. Aside from DWC, there's ebb & flow, nutrient film technique (NFT), and aeroponics. Which is "best" depends on the plant, your budget, and a few things like that. If you tell us exactly what you want to grow, how much of it you want to grow, what kind of space you have to grow it in, and how much you want to spend to build it all we can probably point out exactly what will get you there the easiest.
My best advice on anyone's first-time build of a hydroponic system is this: solve your water transporting before you break ground. Even my little 18 gallon reservoir is not something you can move once it's full. Even with a buddy or two, the only thing you're going to accomplish if you try to move that more than a few feet pushing it along the floor is a big mess. It may only weigh about 140 lbs, but that's a 140 lbs of moving, sloshing water in a relatively flimsy tub. (Plenty strong just sitting there, but it's flexible if you start pulling on it.)
So install a drain valve and flexible tubing that reaches wherever you want the water to end up and work out how you're going to schlep the water to it to fill it. If that means carrying pitchers of water out to it and you're okay with that, that's fine. Just figure it out ahead of time and save yourself a lot of grief.
Here is a link that might be useful: My blog - the DIY DWC is down there a ways.
Q