Super Meter
The three bars at the bottom form a power gauge, a resource for enhancing your moves. You build the gauge by executing special moves, dealing damage, and having your specials blocked.
Use the super meter judiciously throughout the match, mostly for empowered versions of your special moves (sort of EX versions, as called in other fighting games). That's the main method of extending your combos. Don't forget that you need a full bar to use the Combo Breaker.
Practice hit confirming
The tutorial has a section that teaches about hit confirming, which is basically recognizing that your opponent got hit and then finishing or extending the combo.
For example, Scorpion can combo with X, X, X, Left Right Triangle. The latter part is a special move that would leave you in danger if your opponent was blocking, so don't do it if they do.
Mix up your defensive options
There are many techniques you can use on defense after getting knocked down. You can delay your get up, you can call in a Kameo to give you brief invulnerability (usually Left+R1), or you can spend meter to do an armored move.
Keep developing a mind game with your opponent as you play, and switch up your options to throw them off. For instance, jumping is an easy way to avoid both armored special moves or throws on get up.