I would like to say, growing aquarium plants is a like a walk in the park, but the fact is; It is not. Yes you can buy a few plants, stab them in the gravel, and watch them hang on for a few months only to wind up using them in the compost bin. That being said, there are some plants like Cabamba that will grow very well in a normal aquarium setup. The problem with this plant, and a few others are they are very invasive, and will take over your tank. As a matter of fact two lakes by me are under attack by this very plant because someone thought it wood be best to dump their unwanted aquarium plants in the lake rather than just tossing them in the trash. Here is a link to some pretty good advice on the types of plants that are not all that hard to grow.
http://bettasplendid.weebly.com/easy-care-plant-guide.html
Now if you really want to grow aquarium plants to their fullest capabilities; You will need an undergravel heating system. The warmer the roots the better the growth, and longevity of the plant.
Next you will need a good substrate. Fine sand on the bottom, followed by a good planting substrate that can be bought in any aquarium store, and lastly the top layer can be anything from gravel to coarse sand no less than two inches deep.
The next important part is a good filtration system that is no less than three stages, as shown in this link.
http://www.drsfostersmith.com/product/prod_display.cfm?c=3578+3579+16744&pcatid=16744
And last but certainly not least is a good lighting system. many people think they can get by if they just park the tank near a window, and the sunlight will take car of everything. Very bad idea! First you will notice algae growing everywhere. Then as summer rolls around the tank starts to heat at a rapid pace, and finally all is lost because the bio diversity has been nullified, and all the fish die for lack of oxygen. The best lighting is a four tube T5 setup with the proper bulbs for growing plants.
My last tank was a 200 gal tall that was strictly for breeding Angel fish, and growing beautiful plants. I loved that tank, but had to sell it when I was out of work for 2 1/2 years. Hope I don't sound to blunt with my response. What I lack in grammar, I more than make up for with humor.