For starters, fill your bucket until the water is just below the dangling roots. As the bubbles 'pop' they will supply nutrient to the roots.

As the plants grow, back the water level down until the plants are well established.

One thing to remember is you want to leave enough water in the system to absorb some of the heat the air pump generates. This won't be much in the beginning, but as the puddle gets smaller, it starts to heat up the water.

You want to assure the water does not cook the roots. Healthy roots are white. If they start to brown, that spells trouble.

Hope this helps. Just get 'er going and fire questions to the 4m as things progress.

You anyway need to inquire and accumulate some basic knowledge by yourself, through reading and browsing web pages.

Also, when asking questions and advice, please be as precise as possible about the products you use and what equipment you own. Do you have a EC-meter or/and a PH-meter or Kit?

If you haven't got any of these, you simply make sure that the nutrient concentration of your first filling is adequate by following the manufacturers instructions. After that, you simply replace at least 2/3 or maybe 3/4 of your solution every week. If your plants look very healthy and you care about wasting too much, extend it to 10 days. If you want to play safe, simply replace the whole content every week.

If there is a huge consumption (as you say/ for example 1-2 gallon every 2-3 days), replace this amount with a slightly weaker solution (as per default), simply assuming that the water level has decreased and the solution has increased it's relative nutrient content.

If you have got a EC-meter, check the concentration when the solution has decreased in volume by some 1/5 and you'll see if the concentration in nutrients is the same or has changed. You then simply add as much water and nutrient to get back to your initial stet up. The consumption of water vs. nutrient also gives you a clue if you are using the right concentration. If the nutrient content decreases in the 4/5 left, you should raise the concentration - if it increases, your basic concentration of nutrients can be lowered. Still, using this logic you are assuming that you run a balanced NPK-formula, in which you have a balanced uptake of all elements. In reverse case this logic could be inadequate/false. Imbalance of NPK relation can be detected by changing PH over time. The more stable the PH of your nutrient solution keeps, the better your NPK-balance is.

First of all check if the PH is fine, - if it isn't optimal there is no optimal uptake of all nutrients and you run in imbalance and uptake trouble sooner or later, even when changing your nutrient solution weekly!

PS: I am not the right person to ask about products from US or EU manufacturers. As I live in Asia, I am not familiar with any (or most) of them.
Though, there are other members in charge of this domain ;-)