In the past people added nothing to their thanks to fertilize the plants. Then at some point, someone said that plants needed iron to grow, and everyone had to have a bottle of Ferroplant, the only commonly available iron supplement at the time. In the nineties, Dupla additives were introduced and became popular with the addition of laterite to your substrate and Dupla drops to your water. The rational was (and still is partially) that plants received most nutrients through their roots. Fertilizer added to the water was transported to the roots via convection currents. During this time the idea of adding nitrogen and phosphorus to your water was heresy as everyone knew they caused terrible algae outbreaks. A few years later Kevin Conlin and Paul Sears presented an informal study called appropriately enough the Sears-Conlin Paper, where they used a mixture of trace elements, potassium, magnesium, and the previously forbidden nitrogen to fertilize their tanks. The results were that plants flourished and algae retreated in this phosphorus-limited environment. Ultimately a few years later, Tom Barr barbarically shattered the final sacrilege of aquatic gardening. With abandon he added phosphorus to his water, watched his plants grow, and the algae die.
So, which is the winner today? Well, as you might have guessed, despite years of successes with each of these methods and several others, there is still no consensus and the debate continues. If I were to guess, I would say that most people use a hybrid of several approaches. Most plants benefit from the addition of nutrients to the substrate as well as the water column. Additionally whether you limit them or supply them in abundance, plants must have all the basic nutrients to survive. The best thing to do is to get out on the Internet, do some reading, and pick a place to start.
In addition to carbon and oxygen, plants need an array of nutrients. These are usually divided into two groups, macronutrients and micronutrients. Macronutrients are those elements for which plants require significant amounts, and micronutrients or trace elements are those in which only minute amounts are needed. Personally I sometimes think of there being a third or “intermediate” class, which are those that fall somewhere in between.
The macronutrients are nitrogen, potassium, and phosphorus. The intermediate nutrients are calcium, magnesium, sulfur, and iron. The micronutrients are manganese, molybdenum, zinc, copper, boron, and others.
Most aquatic gardeners will agree on the above. The controversy in this area relates to how best to supply nutrients and how much if any need to be added. I will leave the "how much" to your future investigation and will briefly discuss the "how" below.
Depending on your tank's fish load, light, and CO2 levels, enough macronutrients may be supplied by tap water, fish waste, and other decaying matter. However, in high light/high CO2 conditions, these may need to be supplemented. There are now commercial products which supply nitrogen, phosphorus, and potassium in addition to bulk chemicals which can be purchased from various garden centers and hydroponics supply businesses.
Note the elements that make up your tank's GH are about the same elements that make up the intermediate nutrients. Therefore, if you have a few degrees of GH, you usually have enough of the intermediate nutrients. If your GH is low, then there are commercial products available to increase it. If you are creative, you can probably find the bulk chemicals to do this as well. The only exception here is iron. Most aquatic gardeners supplement their tanks with additional iron. Again, commercial products and bulk chemicals are available.
Micronutrients are also available in commercial preparations and bulk chemical trace mixtures. Because so little of the trace elements are needed, many do not give them as much attention as they need. However, many enzymes require these elements to function. Even if only an infinitesimal amount is needed, it makes them no less important. Without them, the plants will languish or die. I personally believe that most people do not dose enough traces.
Once you decide how much of these you want to add from reading more advanced writings, there are two great tools to help you with your calculations. Chuck Gadd's Fertilizer Calculator and the "Fertilator" on Aquatic Plant Central. The Fertilator is somewhat advanced and many of us used Chuck Gadd's calculator for years before the Fertilator came along. I suggest you start with the "Calculator" and move on to the "Fertilator" when you are more comfortable with what you are doing.