The FG is a position that can be both defensive and offensive. Being on your back is an inferior position so the first thing that you want to accomplish is protecting yourself from your back.
One of the most important principles when you have your opponent in your guard is that you must break their posture down. This will give you control so that you can begin your offense. It will also help protect you from fists and elbows dropping on your face.
One way to play the guard no-gi is the Double Wrist Control Guard. Although this guard style has been successful for such MMA fighters as Antônio Rodrigo Nogueira it does not control you opponent's posture and it allows them to sit back in order to drop shots to your face.
You don't want that so you will use many ways to break down your opponent's posture.
Once you have control of your opponent's posture so that you are out of danger you can set up submissions, sweeps or stand up.
One very effective guard style is the Rubber Guard. It has been made famous by Eddie Bravo who is the leading innovator of this guard style.
Check out the techniques and transitions below and train hard !