Here's a
link to the article by Tom Barr that explains the whole clearing with a 50% water change and redosing regimen. Just about anything he writes about plants is worth reading.
Here's a good
article on signs of nutrient deficiency.
If you look at any plant fertilizer in a garden center it'll have 3 numbers on the bottle. My little bottle of MiracleGro says 8-7-6. Thats N-P-K. Nitrogen - Phosphorus - Potassium, otherwise knowns as "Macros" or "Macronutrients". They are the basic and essential plant foods.
Nitrogen comes from the fish (that whole bit with the Nitrogen cycle), but in a heavily planted tank with lights and CO2 and what not the plants may just blow through all of the nitrogen in the tank. You can get all this stuff in bottles online or at a good LFS, or you can go DIY. Spectracide Stump Remover is a DIY favorite for nitrogen.
Phosphorus is the tracest of the macros. Hard to test for and too much can lead to algae issues. You're probably getting enough from the fish food, but if you decide you need to dose a $2 or $3 bottle of Fleet Enema at the pharmacy is most likely a lifetime supply. 2 or 3 drops a week.
Potassium is important and doesn't really have a natural way of getting into your tank beyond the natural levels in your tap water. DIYers use NuSalt from the supermarket.
If you look at the chart in the deficiency article there is a whole bunch of other stuff. Boron, Magnesium, etc. These are the "Micronutrients" or "Traces". Its just not worth trying to find all that sauce in the DIY world when you can just dose something like SeaChems Flourish twice a week.
I also use a capful of Flourish Iron at the weekly water changes.
HTH