Don't worry too much about the 10-point must system; most rounds will be scored 10-9 for a fighter so counting rounds won is usually okay. 10-8 rounds are tremendously rare, so don't expect them to be a factor on the scorecard unless one fighter utterly and completely dominated the round. Rami Genauer of the indispensable FightMetric.com had a thoughtful take on what does and doesn't make a 10-8 round.
While each promotion has slightly different judging criteria, for simplicity we'll just look at the UFC's.
Clean strikes: Look for shots that are landing consistently. The judges look at clean strikes and heavy strikes, but a fighter who's tagging time and time again with leg kicks and jabs will have an advantage over a guy who lands one or two big swings but is mostly getting dodged and blocked.
Effective grappling: The base of effective grappling includes clean takedowns and active guard position. Clean takedowns are pretty easy to spot, active guard is a little trickier. When the fighters are on the ground, notice what the fighter with guard is doing; are they stopping their opponent from landing effective strikes? Trying to reverse or improve positions? Attempting submissions? Look at both fighters and their ability to transition; the fighter on top trying to go from full guard to half guard to mount or side control, and the fighter on bottom trying to reverse that sequence.
Octagon control: Part of it is what it sounds like: is the fighter cutting off angles, moving the other fighter backwards? Are they using the cage to their advantage? Where the fight takes place also factors in. A fighter who wants to keep the fight on their feet earns credit for doing so, through effective takedown defense.
Effective aggressiveness: Blind aggression is a good way to get yourself kicked in the head or trapped in a strangle, but judges will favor a fighter who is pushing the tempo of the match as opposed to one who is simply being passive. Keep in mind that the referee can force the action if both fighters are being passive. PRIDE, when it was active, had a rule that stated that a fighter who drew a yellow card through passivity would also forfeit 10% of their purse. Timidity, however, is a still a foul and point deduction under the Unified Rules.