Rolling dice outside of combat should be kept to a minimum. Below is a partial list of dice rolls and comments about them or their mechanics.
Social Rolls:
For most social encounters, players are expected to roleplay how their character behaves to the best of their ability. Social skill rolls will only be used for trivial situations to save time and keep the game moving. Occasionally they may be used to reinforce game stats (if someone is playing a non-socially skilled character too socially or if a more timid player is attempting to roleplay a socially skilled character). These rolls will augment RP, not replace it.
Intelligence/Wisdom Rolls:
Like with social rolls, if a smart player is playing a statistically dumb character or if a dumb player is playing a statistically smart character, doing these checks is an option for the DM or for player to request. Players should not rely on their stats to make smart decisions or to avoid stupid mistakes. Int checks will give you information and knowledge, they cannot make decisions for you.
Random Encounters:
Traditional D&D favorite. These can happen anytime, anywhere the DM feels like. One player rolls a 1d20. Rolling under or over certain number means an encounter. Generally bigger numbers means larger or more dangerous encounters. Not all encounters are hostile and some encounters can be avoided or dealt with in differing fashions depending on circumstances.
Luck:
Low is bad, high is good. 7 is best! 13 is worst!
Non-Weapon Proficiency Check:
Roll equal or under Ability + Skill level +/- modifiers. Some skills apply a modifier to this roll (usually a penalty for particularly difficult to master skills). If you do not have the relevant skill you either roll at a significant penalty, or may be unable to roll a check at all.
Perception checks:
This is usually an Intelligence check. Alertness, Observation or other NWP may apply. Hear Noise Thieving Ability trumps regular hearing.
Power Check:
class level + 1d20 vs class level + 1d20. Use pertinent class to the situation.
Surprise:
When something unexpected happens, there is a chance you are Surprised when combat begins. If you are Surprised, you do not get to act that round. To check for surprise, roll 1d6: Low is bad but how low depends on circumstances. Usually 1-3 is surprised, 4-6 is not. If you are cautious and might be expecting something (but do not know what), the surprise range could be reduced to a 1-2, 1, or even eliminated. If you are completely oblivious or distracted, the surprise range may be increased.
Who Gets Hit:
If more than one person has a chance of being attacked, all possible targets roll 1d6. Low man gets hit. Or the DM can pick.
Thieving Ability use:
Roll percentile dice. Any result under the percentile score listed, modified by bonuses or penalties from circumstances is a success. Degrees of success may matter. Any roll of 100 is an automatic failure, regardless of your score.
Countering Thief Abilities:
Intelligence plus highest class level in percent as penalty to thieving check. Relevant NWP (Alertness, etc), add +5% per level. Person who has the highest margin of success wins. High-level characters are riskier for a filch, but probably still easy pickings for a thief specializing in that sort of stuff. Usually, when someone is hiding, they are either behind something solid or their presence is completely obscured by full concealment. There is no such thing as hiding in plain sight without the use of magic (like Invisibility). A target who is unaware of a sneak's approach (back turned, do not hear you) automatically grants full concealment condition.
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