To attack line up 3 or more gems of the same color in a vertical, or horizontal, row. You also must have a card on your team of the same color as the matched gems.
A combo attack is a damage multiplier. A new match of three or more gems increments the combo counter. A new gem added to an existing combo does not increment the combo counter.
Affinity Strengths and Weaknesses
Each affinity deals double damage (+100%) against a certain affinity, and half damage (-50%) to another:
Power gems are created by making a single match of 5, or more, gems of the same color. A power gem has a roman numeral on it that displays its level. When power gems are used they do several things: They increment the combo counter, They cause the hero to attack all enemies, and Create team-up attacks.
Swap power gems of any color to trigger a team-up attack. A team-up attack removes all the gems of the same color as the two power gems, attacks all enemies instead of just one, and increments the combo counter by one (swapping the gems is considered a match) plus the number total of the numbers shown on the power gems.
Each hero has a battle skill that can be triggered be tapping on their picture before making the first gem match. The battle skill is ready to be triggered when the ball on the left side of the hero's picture is glowing. The battle meter is filled by making matches and will not be filled up by gems destroyed via a team-up attack.
Each hero you own has a leader skill. This is a passive skill that activates only if that hero is the leader of your team, or if the hero is an ally you have brought with you into battle.Make sure you set up teams with different leaders, and make sure to bring the right leader character and ally into each battle.
For most battles you must select an ally to use in battle. The pool of allies you can select from is first your guild, second your friends, or third some random adventure about your level (rank). The ally’s leader skill will significantly effect the outcome of the battle. After you select an ally be sure to use the info button (the [i] button to the right) to see what effect they have on your team.
(Information is from N3twork's Legendary Starter Guide)