This is the first type of hydroponics system i built: in it's first form , probably the easiest and cheapest to build.
I originally based it on this and this (very nice instructables).
-One or more plastic bottles
-Saw to cut out the bottom of bigger plastic bottle to fit the small ones in(i used a 60 mm one, standard plastic cups fit right in) (5euros for a set of 6 different diameters) (this may also come in handy to cut out the board where you will place these bottles)
-Air pump : standard aquarium air pump (around 20-30 euros for a Rena pump) (for the first version)
or
-Water pump (any sufficiently powerful water pump)
-A few meters of 1/4" silicon tubing (at any aquarium shop, or better, at gardening shops, since they are usually WAY cheaper)
-Basic plastic cups : you will need to drill/melt a few holes and cut the sides a bit to let the water and the roots through
The rest of the list is purely dependent on your specific needs:
-Depending on whether you will beĀ doing your culture indoor or outdoors you might need some lamps ( i just bought some relatively cheap (19 euros) 13W/50 cm fluorescent tubes, not sure on how fine that will go , but well)
-I also had to build a door and some walls to provide some protection of my tiny flat from water projections/ isolate the grow box a bit
-Some sort of sheeting /aluminum foil to protect the roots from the light
-A kind of stand/structure to hold your home made watering system in place (i found (on the street!) a 1/1m 5mm thick plank which was just perfect for that
So i have divided my available shelving place (30*35 *180) into two compartments :
-upper shelving : 30*35*85
-lower shelving : see part two
I went through a bit of trial and error, and tried to make a maximum use of what i had in hand, so it is far from perfect: ( i actually bought WAY to much material compared to what i actually needed in the end)
-The air pump solution is the cheapest to build, but a bit hard to manage precicely
-I decided to add the overflow protection system later, which came with its own handful of problems
-This really is my favorite system as far as flexibility goes