Well, there are user combos and auto combos.
User combos are like so; you swoop into someone with no mouse buttons held to begin adv. melee. Your character will start autopunching the opponent. If you press either left or right click, you will stop autopunching and will see a bar appear at the bottom of the screen that fills to the right depending on how many autopunches you did. Holding a mouse button chooses either punch or kick, and pressing a direction with your movement keys chooses the specific attack.
Say you hold left click and press W(up). You have added a high punch to the bar, represented by a green portion of the bar with a blue arrow pointing up above it. Then you hold right click and press left. You have added a left side kick to the bar, represented by a green portion of the bar with a yellow arrow pointing to the left above it Depending on how long you wait to press a direction, you will add power to the attack; the longer you wait the more powerful it is. A light attack is represented by a green bar, a medium attack by blue, and a strong by red. The stronger the attack, the lower chance your opponent has to defend against it, which I will explain later.
When the bar has filled all the way to the right, you will see your character execute the combo. While this is happening, your opponent will see all the directions you pressed scroll by at the top left of his screen. He must press the same directions you did in the same order to block your attacks; for each incorrect press, that hit connects. Now, depending on the power of your attack, a multi-directional arrow will appear in place of one of the directions you pressed; the stronger the attack, the more likely it is to be random. If your opponent guesses wrong, that hit connects. After they are done blocking, they will have a chance to retaliate with thier own combo, which you have to block in the same fashion.
Auto combos; kinda cheap at first, but if you know what they are, they are easy to block. Auto combos are performed when you press a series of directions with the proper attack, punch or kick depending on the combo. Combos have 3 or more directions, and if one of the hits gets through, your character will do the combo. The auto combo, once started, is unblockable. As for the directions, well, I can't come right out and tell you. I will give you a clue though; DBZ characters must have learned Shotokan-style karate between 1.1 and 1.2.
Good luck!