The first thing to know about is proficiencies (profs for short). Proficiencies are abilities that can be used in and out of combat. They include magic, skills, and weapon proficiencies. In order to carry out an action that requires skill, you’ll need to make a check. Your GM will roll the die for you but it helps for you to have an idea as to what will modify your chances of success before you go into it.
The more challenging or complicated a task you are attempting, the higher the DC for the roll. That means you’ll need to roll higher to succeed. Conversely, the more points you have in the applicable proficiency, the lower the DC and the easier it will be to succeed. You can even roll for a (non-magic) skill you have no proficiency in but you won’t have a very good chance of succeeding on anything too tricky. If you have a 3 or above in a prof, not only does that lower your DC but you’ll get an advantage on those prof checks as well. That means the CM will roll twice to see if you succeed and take the highest roll. Likewise, a disadvantage is when the CM rolls twice and takes the lowest roll. If a prof is rolled with both advantages and disadvantages, one disadvantage will cancel out one advantage.
Proficiencies above 4 will confer a special ability related to the ability’s use, identified as a mastery. Players are allowed one mastery of a proficiency, adding to the effectiveness of that ability's action and offering an advantage or duplication of the original level 4 bonus.
Practically any roll you make is going to fall under one of the four base statistics: strength, speed, magic and skill. If you have advantages in the relevant statistic, you'll roll with those advantages as well as any advantages you have in the proficiency. These stack. This is of course, also true for disadvantages so be careful. When taking multiple actions in one round, you'll need to succeed on a speed roll using your speed stat to avoid fumbling and not accomplishing anything for the round. If you are trying to do two things at once, the speed DC is 5. For three things, the DC is 10. For four things, the DC is 15. Certain proficiencies or other aspects of your character can alter how many actions you can take in a turn and what the speed DC will be.
For example: Archenteron the Mage is a master of wind magic, a fairly skilled acrobat but truly no fencer. That is to say, he has a 4 in air, a 2 in acrobatics but no points in blades. If he were to try something mundane with air like firing a common lightning bolt (something air magic users uniquely can do), he’s pretty likely to succeed. The DC for that task isn’t that high regularly and his high skill level brings it down significantly. Combine that with the advantage he gets for having the skill above level 3 and he’s got this attack in the bag. If he tries something more grand in scale like creating a hurricane out of a clear sky, he’s still going to have the advantage but the very high DC for such an act makes it a toss-up as to whether or not he’ll succeed. With a sword, even the most simple slash will require a reasonably high roll to succeed because he isn’t proficient with it. To accomplish something like a spinning attack that strikes four enemies at once would require either a natural 20 or just be completely beyond his reach. As you can imagine, performing front flips and handsprings would fall between these two extremes for him.