This design has a few features that distinguish it from others. One is the height of the barrels. The height allows me to water my garden without having to do it the old-fashion way (filling and carrying watering cans).
Another distinguishing feature is the automatic overflow system. When the barrels are full, the rain continues to cycle through the barrels, but the overflow is sent through the gutter downspout. Other designs may have some kind of manual over-ride, but this design is completely automatic.
Step 1: Build platform
When I built the platform, I thought long and hard about safety. . Making a safe platform isn't an impossible task, but 800# (density of water is 8 #/gal) is enough to be careful about. Several things to keep in mind are the strength of the decking material, the height of the tower compared to it's length and width, and the strength of the legs.
I used standard 4x8 retaining-wall block for my first attempt. It was tippy and I took it down immediately. My second attempt was pairs of concrete block, alternating. The second time 'round, I decided to use sand as the base material for the legs. It made the whole job much easier and the cost of the sand was small.
I made the platform out of bits of lumber from an old deck. Using re-claimed wood is cool, but this may not be the place for it. My deck turned out strong enough because I used two layers, but I recommend using decent wood.