Grappling has a lot to it and there are many methods. What I will do is explain grappling the way I teach it. There is logic to my madness.
First, I want to be 100% clear, I am not teaching grappling for you to go into a ring and compete. I am teaching grappling so you can dominate your opponent(s) in real life.
Second, the journey is long and very much worth the end result.
I break grappling down into this:
Basic Grappling  –  You learn to break holds, break holds and follow-up, in some cases reverse them and place them in a hold (one far superior to the one you were in), and use your opponent as a shield against other opponents. 
Advanced Grappling  –  (aka. wrestling, judo, jiu jitsu) This is where you are learning a wide range of takedowns.

• Hawk Down =  Impacting a high and low point simultaneously to knock a person to the ground. This is typically one of the harder falls for an individual to take.
  
• Sweep =  An action that will remove a or both pillars (legs). The contact is usually below the knee joint to make this successful and effective.
  
• Leverage =  This is an action that is either hinging or locking on their body allowing a small movement on your part, thus creating a much larger reaction on their part to guided them to the ground. In most cases, by increasing velocity a break is probable and the take down is not always assured.

 3D Grappling  –  This is where we go back to the basics and add movement and direction to what we are doing. As this gets more practice a natural “personal refinement” occurs. There is really 3 parts to this. How you move and its effects, the openings and closing of opportunity. How your opponent responds and can move, its effects, and the openings and closing of opportunity. And of course the last stage, both you and your opponent interactive moving and knowing what will be open or soon to be open yet aware of your potential weaknesses along the way.

Seamless Integration  –  This is where you can do grappling from any position, repeatedly fell somebody, and it naturally works with your kicks, strikes, grappling, and felling (aka. 4 ways of fighting)