While I am not an expert, I have fumbled through about 9 months of hydroponic gardening (as of May 2019) and may, at least, be able to help other beginners from repeating my “opps!’ moments. Luckily, I have had the help of my lovely tutor, “Google”, and her somewhat-trusty sidekick “Youtube”. I would suggest you utilize this team as well, but in the meantime, here are some of the basics…
Hydroponics is pretty much what is sounds like, growing plants in water. I don’t know the science behind it, but in general, hydroponic plants grow faster and yields more than the same plants in soil with the same conditions. There are, I believe, six main types of hydroponic systems that are used: 1) the wick system, 2) the ebb and flow system, 3) the nutrient film technique (NFT), 4) the water culture or deep water culture (DWC) system, 5) the drip system, and 6) the aeroponic system. This website has a pretty good description of all the systems and how they work. I personally use the ebb and flow and DWC systems, depending on the needs of the plants.
Additionally, one of the easiest and cheapest ways to get into hydroponics is the Kratky method. Developed by B. A. Kratky, this is a passive hydroponic system which is also described as a DWC system without the air pump. More information could be found here. You are, however, somewhat limited by what you can grow, which is mostly leafy greens. Lettuce is known to do very well in Kratky systems.
Literally Homegrown 