The myriad of possible actions taken by the player characters or other actors in a milieu is innumerable. Likewise, the circumstances to be faced in the campaign environment are legion. To attempt to draw up rules for all specific actions or environmental obstacle would take up an entire book (several, actually).
However, for a DM in a hurry, there are several important principles required for such rulings.
Be consistent. While circumstantial modifiers may change, the basis should be understood. This helps to mitigate any assertions of bias. In essence, the DM must “pick a system” to use for different action types. The system itself is not as important as the fact that it is used consistently.
Reward a player’s effort. A big part of the “fun factor” of the game is player creativity used to overcome odds stacked against them. A good DM will understand this and take into account player actions (no matter how silly or strange) when adjudicating actions or circumstantial modifiers. Furthermore, characters that take the time (out of adventuring), expense, and effort to seek out and obtain training (to whatever level of skill), should be rewarded for this cost (and the DM will be sure to assign the cost).
Where possible, avoid random rolling of dice. This is to simply say, if the character has a reasonable chance of success and circumstances are in their favor, allow the character to succeed without rolling dice. The DM will make the call based on the situation (particularly where the risk of failure has material effects).
Assign a Difficulty. This is the base chance to succeed before modifiers. This could expressed as a percentage or a chance to succeed on a d20 roll (0, 5, 10, 15, 20 or more) or it could be an Armor Class needed “to hit” or a particular save (“normal” using Petrify or “difficult” using Breath). Untrained characters trying to accomplish a task normally requiring training (such as thieving) should have, at maximum, half of the standard chance (if indeed, any at all).
Assign Modifiers. Adjust based upon character attributes or background. Typically totaling -4 to +4 on a 20 point scale (although circumstances may warrant a broader scale). The DM will take into account the character’s racial attributes, class features, ability scores, secondary skills, back story, and other personal circumstances (armor, encumbrance, etc.) when assigning modifiers to a chance to succeed.
Life-or-Death Attempts. It is usually good practice for attempts that fail that would result in immediate death to offer some type of saving throw to avoid the death (catching oneself, etc.).
Example #1. The elf Fonkin (an 8th level fighter/magic-user) has surprised four human guards standing outside of a Keep entrance. It is night and they stand clustered around a torch on one side, sharing a pipe. The portcullis is partially open, allowing the guards to move behind and quickly lower it. Fonkin wishes to move quietly past the guards and slip into the keep unnoticed. The elf forms a quick plan; He will sneak up from the side opposite the torch and toss a pebble over the guards to draw their attention, he will then slip in. Furthermore, the elf pads his equipment using sacks and drapes his dark cloak about himself. The DM determines that the night is windy, the moon is half, and the ground is rocky, being strewn with gravel. The guards are not especially attentive. Fonkin is wearing chainmail armor (negating his bonuses to surprise, but the armor is magical). The DM decides to assign a base difficulty of 20 on a d20 roll (due to light conditions, normally, this would be impossible) modified by the rocky ground (-2) and wind noise (+2). He grants the elf a racial bonus (+2), armor penalty (-4), a Dexterity bonus (+3 for 18 Dex), and a circumstantial bonus for distracting the guards (+2). Normally, this would be a 15% chance to succeed (17 or higher on a d20). If Fonkin removes his armor, this would jump to 35% (13 on a d20; and still less than half the chance if Fonkin was a trained thief).
Example #2. Drudge the 1st level human fighter has come to a 15 foot fissure blocking the dungeon hallway. Vines hang from the walls and ceiling and water rushes by 40 feet below. Everything is damp. The hallways are straight on either side. Drudge decides to take a running leap across the fissure using the vines to help him make the distance. Drudge wears splint armor. To help his chances, he takes this off, puts it in a bag and ties this to a rope he attaches to his belt. (Once across, Drudge wants to drag the bag of armor over rather than risking throwing it over.) Drudge spends time (risking encounter checks) selecting the thickest looking vine to grab during his jump. The DM assigns a base difficulty of 15 on a d20. Modifiers are dampness (-1) and the rope tied to his belt (-1). Because Drudge worked as a sailor in his youth, the DM determines he has experience jumping and using ropes (+3). Assuming Drudge uses a vine, the DM determines he will need to hit an Armor Class 10 attack but this will give him an extra +4 to his jump attempt. However, if he misses the vine, he will fall. The DM further decides that, given this is a life-or-death attempt, a failed roll within five of the required number for success will grant a Petrification save to grab a hold of the opposite side. Drudge must roll a d20 twice with a result of 10 or higher to succeed.