In this section, Moldvay says:
"The DM may want to base a character's chance of doing something on his or her ability scores (Strength, Dexterity, and so forth). To perform a difficult task (such as climbing a rope or thinking of a forgotten clue), the player should roll the ability score or less on 1d20. The DM may give a bonus or penalty to the roll, depending on the difficulty of the action (-4 for a simple task to +4 for a difficult one). A roll of 1 should always succeed, and a roll of 20 should always fail."
Not only is this an elegant way of handling all those little actions in the game that shouldn't be an "auto-success", its also a good way to put emphasis on those six ability scores, which otherwise really only come into play on a regular basis for combat resolution. It also is a handy tool to get players who have only had later edition gaming experience get over the mindset that a character has to have a particular "skill" rating to do something like decipher some old runes or catch a fish.
This is such a simple little resolution system, its easy to overlook how huge of an impact this can have on your game, again reinforcing creative play. When players have the mindset that "There's always a chance", they should actually start taking those chances more and more.
It might be a good idea to read the above quote aloud at the beginning of each session, just to remind everyone and keep the concept fresh in the players' minds as the night's adventure begins. When the players are actually looking for something to test their "skills" against, it leaves a whole lot less empty space for the DM to fill.