Hi, Panda Cory.
There are many benefits to real plants over fake plants. A couple are, they tend to keep your water cleaner, and they add oxygen to the water. Plus, usually, the fish just like them, to swim around in, or sometimes nibble on. Sometimes, however, plants can take a little extra work.
The answer to "how do I take care of plants" is, at the base, pretty simple. Clean water is important, but you're doing that for the fish in the tank anyway. After that, there are three main things that you have to keep balanced -- lighting, CO2 (carbon dioxide), and nutrients.
If that sounds kind of complicated, don't worry about it too much yet. Read until the bottom.
The amount of lighting you have will determine what kinds of plants you can grow. Some aquarium plants need tons of light (much more than what you have with a standard store-bought tank setup), and some don't need much light at all (that is, a 'regular' tank light will do just fine). If a plant doesn't have the light it needs, then that will limit its growth -- sometimes to the point where it dies.
When a plant has plenty of light for its needs, then usually the limiting factor on growth is CO2. During photosynthesis, plants turn CO2 into O2 (oxygen). When a plant has plenty of light, but not enough CO2, it will also have problems growing.
When a plant has plenty of light and CO2, then it usually does well, if it has enough nutrients. These nutrients are things like potassium, nitrogen, phosphorus, and iron. The stuff that's usually in fertilizers, for both aquariums and outdoor plants.
So, you might think that having healthy plants means you need to add tons of lighting, lots of CO2, and a whole glob of fertilizers. That's not necessarily true. That's what you'd need if you wanted to grow
any plant, or "difficult", "high-light" plants.
But, as I mentioned, it's all about balancing those three factors. If you find and get plants that require little light, then chances are they will get enough CO2 'naturally' from the water, and will probably also get enough nutrients from the water.
So, after all that, the short answer is, if you do research beforehand, and pick the right plants for your conditions (which is usually "low-light" plants), you should be able to successfully grow plants without ... well, without really doing anything special, except maybe trimming them when they grow too large, and maybe adding a little fertilizer.
That is, if you just pick up some random plants, chances are they won't do very well, but if you start with the right plants, they can easily almost "take care of themselves".
Of course, that's kind of simplified, and there are some specifics that come into play, but that's the general idea.
One place I'd start research is at the
Plantgeek site. They have a very good Plant Profile section, that lets you sort plants according to light needs, and difficulty. Plus, most of the plants have pictures.
Hope that helps.