Checks are made whenever a character attempts to do something that requires effort. They are divided into two types: standard checks and opposed checks.
Standard checks are checks where the character is trying to overcome a static, or relatively static, obstacle of some sort. This can range from searching for a man in a crowd to defusing a pressurized bomb without tools. Players roll 2d10 and compares it to their character's effective skill or stat level (the base stat plus any applicable skill ranks or modifiers). In many cases, modifiers will be based on another character's skill ranks, or their stat's distance from the standard 10. Successes occur when the roll is less than or equal to the character's effective level. Failures occur when it is more than the character's effective level. A roll of 2 is always a success, while a roll of 20 is always a failure.
Nathan, a thief, wants to pick the lock on a chest. His Skill is 12, and his Thievery is 2. However, the lock is very well-crafted, and has a modifier of -3. His effective level is, therefore, 11. He rolls 2d10 and gets a 14, thereby failing his check. The lock remains locked, and the loot within is safe.
Opposed checks are checks where two or more sides are actively opposing each other. This can range from a short spar between friends to a puzzle-solving competition. Each character (or group of characters) involved rolls 2d10 and comparies it to their effective skill or stat level. The one furthest below their effective level succeeds, regardless of any 2s or 20s. The number they succeeded (or failed) by is referred to as their margin of success. If two or more sides have the same margin of success, all tied sides re-roll their check and compare again.
Before Nathan can try again on the chest, the hired guards burst in and start chasing him through the lantern-lit street, separated into two groups. Nathan's Agility is 12, while the guards' is 11. On the first roll, Nathan rolls an 8, while the two groups of guards roll a 7 and a 9. Since both Nathan and the first group of guards have a margin of success of 4, they re-roll the check, getting a 14 and a 15, respectively. Therefore, Nathan makes a narrow escape as his margin of success is -2, while the remaining guards' is -4.