Unlike in B/X and other versions of D&D, all skills use the same table. By default, all skills advance according to the "Good" progression. (See table at the bottom of this post.) However, a thief may choose to reduce a skill to Basic in order to become Elite in another.
Each skill has an associated ability score which may modify the chance of success, if desired. Each point of bonus or penalty equals a 5% adjustment, so +1 = +5%, +2 = +10%, and +3 = +15%, with negative modifiers exactly the opposite. Ability modifiers are optional; if the GM prefers that the percentages be used as-is, ignore them.
The skill list below is divided into two parts, Thiefly Skills and Other Skills. The first is the default array of skills for the thief class. The second is a supplemental list, which may be used to modify the basic thief to a more general "Expert" class. Characters of all classes are allowed a secondary skill to bolt onto their core class abilities, and may choose one from either list. Thus, you can quickly make, say, a fighter character into a ranger (Tracking), a holy warrior (Divine Piety), a combat medic (Herbalism), a stealthy scout (Stealth), or a herald (Lore.)
All secondary skills are at Good level, unless modified by a class or race feature. (For example, all halflings have Stealth at Basic level. A halfling taking Stealth as a secondary skill adds that to his default Basic, and gets it at Elite level.) Optionally, if the GM allows it, a character may take two secondary skills at Basic instead of one at Good.
Note that secondary skills are skills that will see much use in an adventuring career, and are effectively part of a character's profession. They do not include, for example, background skills of a profession practiced before the character became an adventurer which are only rarely applicable to adventuring, nor skills which have negligible mechanical effects on play like music or etiquette, nor skills primarily of use between adventures such as blacksmithing or animal training.
I've deliberately kept the list fairly short and focused, for a couple reasons. Firstly, because character creation shouldn't be an agonizing process, and the GM shouldn't have to remember what dozens of different skills do. Secondly, because I want them to be useful, in conjunction with the basic classes, for building archetypal characters, something which becomes difficult when you must have multiple skills to affect the archetype you want. If, for example, there's a separate skill for survival in each type of wilderness terrain, in addition to tracking for wilderness and underground, then your ranger character arguably isn't complete without all of them, and that would torpedo the simplicity of character creation.
It would certainly be possible to use the skill table and general principles (doubles or tens digit degree of success) for tasks in which all adventurers are assumed to be proficient and improve with experience. For instance, if all adventurers know how to survive in the wilderness in your game, it's trivial to look up a character's level on the table and roll the dice against the listed percentage to see if she finds food, with the tens digit representing the number of character-days of food obtained, or doubles on a failure resulting in poisonous or tainted things mistakenly identified as safe and edible.
It's also easy to allow any character a marginal chance to succeed at any skill. Just use the 1st level Basic line for any skill the character doesn't actually possess, i.e. a base 10% chance of success. (This purposely doesn't allow for success with doubles!)
The standard thief has the following skills by default.
Tinker (Int) is a knack for things mechanical, and encompasses the old skills of opening locks and removing traps. Normally each Tinker attempt takes one turn (10 minutes.) Rolling doubles on a success reduces the time to a single round (10 seconds.) Doubles on a failure jams the lock or sets off the trap.
Stealth (Dex) mashes together the abilities of moving silently and hiding in shadows. A stealth roll is made only when some person or creature has a chance of noticing the character. Doubles on a failure indicates that the character has inadvertently done something to draw attention, such as knocking something over. Stealth is not possible when wearing medium or heavy armor.
Climb (Str) allows a character to ascend sheer surfaces, as long as the surface is rough enough to provide hand- and foot-holds. A climbing roll is made at the beginning of a climb. The tens digit of the roll gives the number of rounds the character may climb before making another roll (on a success) or the number of rounds the character is stalled and looking for a way forward (on a failure.) Normal climbing movement is at 1/4 the character's normal movement rate per round. Doubles on a success allows double climbing movement until the next check. Doubles on a failure result in a fall after covering half the distance. Climbing is not possible while wearing medium or heavy armor.
Alertness (Wis) is similar to Hear Noise. It isn't the ability to hear, per se, but rather the ability to interpret what is heard, making sense of the obscure mumblings behind a door or recognizing the significance of an anomalous sound from amid background noise. Alertness is not possible when wearing medium or heavy armor unless the helmet is not worn (-1 penalty to AC.) Time required: 1 round.
Sleight-of-hand (Cha) allows the picking of pockets, but also juggling, simple faux-magic tricks, and any other gambit that requires quick fingers and misdirection. Each attempt takes one round (10 seconds.) When used to take items from an unaware NPC, the roll is penalized by 5% for each level of the victim above 5th. Each success procures one item. Rolling doubles on a success nets an additional item, while doubles on failure means the attempt has been noticed. Time required: 1 round. (Why Charisma as a modifier? Because picking pockets is often about misdirection rather than pure stealth - engaging your mark in distracting conversation while you surreptitiously loot him, staging a convincing "accident" as an excuse for invading his personal space and possessions, or simply looking nonchalant in a crowd while your hands are busy in the lady's shopping basket. Substitute Dex if you prefer.)
Cipher (Int) is the ability to puzzle out codes and unfamiliar languages. Rather than gaining a flat 80% at 4th level as in B/X, it is gained at level 1 and improves like any other skill. The tens digit of a successful roll indicates the number of questions about the document that the player may ask and have answered by the GM. (If the tens digit is 0, the GM chooses one piece of information to give the player.) Time required: 1 turn.
The following skills are not automatically gained by thief characters, but rather may be taken by characters of any class as secondary talents.
Lore (Int) is knowledge of the campaign world and its history. When a lore check is made, the tens digit of a success indicates the number of questions that the player may ask and have answered by the GM about a particular topic. (If the tens digit is 0, the GM chooses one piece of information to give the player.) Time required: 1 round.
Tracking (Wis) is the ability to follow the trail of some individual or group, or to cover the tracks of oneself and/or one's party. On a successful tracking check, the tens digit of the roll indicates the number of questions the player may ask and have answered by the GM. For example, what kind of creatures, how many, how quickly were they moving, which direciton, were they encumbered, etc. (If the tens digit is 0, the GM chooses a piece of information to give the player.) Time required: 1 turn.
Herbalism (Wis) skill may be used to make healing salves, infusions, poultices, and such, to treat wounds, disease, or poison. A concoction must be made for a specific purpose; it does not work for all afflictions at once. The tens digit of a successful roll indicates how many points of damage are healed or a bonus to saving throws to overcome poisoning or disease. Time required: 1 turn.
Arcane dabbling (Int) allows a character to use magic items normally usable only by mages, including wands and spell scrolls, on a successful roll. Doubles on a failure result in a mishap, possibly spectacular. The character also gains limited spell-casting ability, and may attempt to cast a number of spell levels per day equal to half his or her level or Intelligence bonus +1, whichever is less. Thus, a character with 16 Intelligence could use one level 1 spell at 2nd level of experience; at 6th level she could attempt up to three level 1 spells, or a level 1 and a level 2, or one level 3 spell. A roll must be made, with the same chance of mishap on doubles as for item use. Failed spells still count against the day's total. Time required: 1 round.
Divine piety (Wis) allows the character to use items normally reserved to clerics on a successful roll. Doubles on a failure means that the gods are angered and the character suffers a curse. The character may also attempt to pray for divine favor (i.e. cast divine spells) a number of spell levels per day equal to half his or her level or Wisdom bonus +1, whichever is less. A roll must be made, with the chance of angering the gods as above. Unanswered prayers still count against the day's total. A character who abandons his or her faith loses all associated abilities. Taking up a new faith may restore the benefits of piety, at the GM's discretion. Time required: 1 round.
Skill Advancement by Level
Level Basic Good Elite 1 10 20 30 2 15 28 40 3 20 36 48 4 25 44 56 5 30 50 64 6 35 56 72 7 39 62 78 8 43 68 84 9 47 72 90 10 51 76 94 11 54 80 98 12 57 84 102 13 60 86 106 14 63 88 110 15 66 90 113 16 69 92 116 17 72 94 119 18 74 96 121 19 76 98 123 20 78 100 125