In short, roll a d20, add your bonus.
If attempting to use a skill outside of combat, when not under pressure, you can “take 10” – treat your skill check as if you'd rolled a 10 on the dice. There is also “take 20” for skills with no negative consequences in the event of failure.
You can also aid another if you try a skill check on something your friend is doing: roll 10 or higher, they get a +2 bonus.
If attempting to perform a task that does not correlate well with a skill, use your ability modifier instead, e.g. adding strength mod to kick down a door, constitution for holding your breath, etc.
Each round of combat is 6 seconds in length. Each grid square is 5 feet.
Choose among the following:
Attacking an enemy is a standard action.
1d20 + stated bonuses (BAB, str/dex mod) vs enemy AC. If the attack lands, roll for damage.
Critical attacks work like this: if you roll a 20, roll a regular attack roll again. If it lands, roll your damage roll twice; if it misses for the second time, just roll your normal attack die. Rolling a 1 is a critical failure: your attack fails.
Making an attack, helping a friend, drinking a potion, lighting a torch, casting a spell, using a skill etc are all considered to be standard actions. You can also choose to defend yourself, adding +4 to your AC.
Speaking, drawing a bow, dropping an item, or falling on the ground are all free actions.
Drawing a sword, reading your bow, etc are considered to be move actions unless you have a BAB of 1 or more. Readying or loosing shields are move actions. Standing up is a move action.