Three things are needed for plants in general to thrive.
They are: Food, Water, and Light.

LIGHT

In the wild, light is available in a limitless supply. In the aquarium however, we must supply it and supply it in sufficient quantities to be useful. For most plants, and most tanks 2 to 3 watts per gallon is a good amount. More light is needed for deeper tanks and for brighter lighting requirements. Once the intensity need is fulfilled, spectrum and duration need to be met.

Plants need light that is on the red and blue part of the spectrum. This is where Flourecent lights work better than incadecent lights, because the spectrum can be determined simply by placing different material in the lamp, while regular light bulbs tend to be more yellow and less suitable for plants. Keep in mind that all visible light will work for plants because it contains the correct light for them in some amount. But if you can provide more of the desired light, they will do better. There are 2 common ways we identify the appearance of light, the color temperature, and the Color Rendering Index (CRI). The color temperature (measured in degrees Kelvin) is what closely applies to the actual spectrum of the light. If you use light with a color temperature of 5500K to about 7000K, your light is the correct spectrum for fresh water. The CRI of a light indicates how closely matched the colors are to the same colors in true sunlight. This scale uses the sensitivity of the human eye, and since our eyes are more sensitive to the green part of the spectrum, a high CRI is not necessarily what you want for a planted aquarium.

Most of the aquatic plants come from parts of the world where the sun shines for 10 - 14 hours each day, depending on the time of year. That is what we need to use for our standard. Remeber this: duration cannot be a substitute for intensity.

FOOD

Food is processed by plants through a process called photosenthesis. The amount of photosenthesis that occurs is directly determined by the amount of light and CO2 available. Temperature also plays a roll in this process but not a significant part.

What basically happens is the plant gathers trace elements (iron, calcium, zinc, phosphate, etc) through the roots or leaves and collects CO2 from the water through the leaves. These elements are then broken down and processed into sugars, releasing oxygen as a by product. The sugars are used to feed the plant and support it both during the day and night. If any of the required elements are missing, the plant will suffer. An excess of any of these elements will result in algea problems.
To see an article by Tropica about the CO2 relationship go here.
To see a CO2 table by Tropica go here.

There are macro nutrients and micro nutrients, which the the plants need. They are as follows:

MACRO Nutrients:

Nitrogen - needed to produce amino acids and essential for cellular structure. Nitrogen is relocatable within the plant.
Phosphate - needed for the production of nucleic acid, storage and transfer of energy within the plant, also needed for the production of the cell membrane and root formation, also mobile within the plant.
Potassium - activates enzymes, essential for sugar translocation and starch production, also mobile within the plant.
Calcium - needed for the cell wall and mebrane integrity. mandatory for new cell formation.
Magnesium - the central cation in clorophyll.
Sulfur - needed for amino acids.

MICRO Nutrients:

Iron - needed for energy enzyme reactions and the process of photosynthesis. Iron must be chelated in order to be utilized by plants.
Zinc - needed for the majority of enzymes and synthesis of auxymes.
Manganese(Mn) - most enzymes, a deficiency is indicated by brown spots.
Copper - enzyme activator, needed for the processing of vitamin A and production of pigment.(use this with extreme caution as it is deadly to fish).
Boron - needed for new cell formation and processing of carbohydrates.
Cloride - needed for photosynthesis, counterion for neutrality and osmotic regulation.
Molybdenum - mandatory for nitrogen usage and amino acids.

Most of these elements are replenished through water changes, or fish food (phosphates). Some may still need to be added. If any of these elements are missing, the plants will have noticable issues, like holes in the leaves or bad color.