Aquatic plants are like land plants. They need about a dozen elements to live.
Some of these elements are supplied in the water.
Hydrogen (H), oxygen (O).
The element that plants (both land and water) use the next most is Carbon (C).
Plants take in carbon best as CO2, but can use other sources. About half the aquatic plants we keep can use carbonates as a source of carbon. Many plants can use a product sold as Excel. A few plants do not like this material. The amount of CO2 that is dissolved in the water from the air is rather low. Enough for a low tech tank, but the more light you add the more carbon the plants will demand.
The elements that the plants use in the next largest amounts are referred to as Macros.
These are nitrogen (N), phosphorus (P) and potassium (K).
Nitrogen can be taken in from the water and through the roots. Aquatic plants can use ammonia, nitrite and nitrate as sources of N. Protein such as found in fish food, fish waste, and ammonia eliminated via the gills are the largest sources of ammonia in a low tech tank. If these are not enough you can add N from fertilizers.
Phosphorus is also available in fish food and other sources. If there is enough nitrogen from fish food, then there is likely enough phosphorus, too. If you have to fertilize with N, then you should also fertilize with P.
Potassium is usually the fertilizer that is lacking in most low tech set ups. There is not much in fish food so adding K as a fertilizer is often where you get started with learning about fertilizer.
The next group of elements plants need are secondary nutrients. Calcium (Ca) and Magnesium (Mg) are two of these. We test for a combination of these when we test the GH (General Hardness) of the water. If the GH is at least 3 German degrees of hardness, or about 60 ppm, then it is likely that there is enough Ca and Mg in the water. Fish food supplies only small amounts of these. Water changes supply the most. If the water has them. There are some waters that are unusual, and may have a lot more of one or the other of these minerals. Plants use them in a ratio of about 4 parts Ca to 1 part Mg. The water does not have to be exactly that, but somewhere close is good. If you suspect your water is lacking one or the other of these, then you can get a separate test for Ca and look up a formula to figure out how much of the GH is Ca and how much is Mg, then supplement for the missing element. If you know your water is lacking both, then add a GH booster like Seachem Equilibrium.
Another element that plants use enough of to call it a secondary nutrient is iron (Fe).
Fish food does not supply enough. Many trace mineral blends have iron, but some people find they do not have enough. You can supplement iron separately from the other trace minerals, and this is usually the second thing that a low tech tank needs. One store-bought product called Leaf Zone contains potassium and iron. It is a reasonable way to get started, and you can see if your tank is going to respond to these nutrients. Then add Excel (carbon source).
The last group of elements that plants need are lumped together as trace minerals or micros. Plants need these in very small amounts. Excess can be toxic. Most of the time fish food and water changes are a reasonable source of these elements in a low tech tank.
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Source of fertilizers:
If you buy a bottle of fertilizer at the store you are buying a lot of water and just a little active ingredient. That is OK at first. Do this, and figure out what your tank needs. Some products are combined, and this is not really the best, but if that product offers exactly what your tank needs, then go for it.
Better to get each element separately, then you can balance the dose to your plants' needs. Seachem is one company that makes a full line of fertilizers, most bottled separately. Their Flourish product line includes:
C (Excel)
N, P, K, Fe (as separate items)
Ca, Mg, K (combined, as Equilibrium)
Traces (combined)
Read labels on other products, too.
Dry fertilizers that come from the agricultural industry are a lot more economical than paying for a bottle of water with just a dab of active ingredient.
The most common materials are:
KNO3 (source of N and K) If fish food supplies most or all the N, then you won't add much of this, so the K would not count. If the tank needs added N, then the K can be substantial, too.
KH2PO4 (source of K and P, but used in small doses so the K hardly counts)
K2SO4 (source of K) If your tank does not need enough N to use much KNO3, then this is a good source of K.
GH booster such as Equilibrium. Adds both Ca and Mg. Many GH boosters also add K. Some have a few traces, but not much.
Calcium chloride, Epsom salt, other materials: Sources of Ca or Mg separate from each other, just in case your tank needs just one or the other.
CSM+B is one dry trace mineral supplement. It has some iron, but many people add a little more iron.
Chelated Iron (Source of Fe) is a way of binding the Fe to other molecules so it remains available to the plants.
