Attributes, What are they used/rolled for?

When is Dexterity Used?

Dexterity is probably the most valuable attribute in the game, especially for characters that plan to get in a lot of fights.
Defensive actions usually take Dexterity + Melee, Dexterity + Brawl, or Dexterity + Dodge.
Attacking with a sword or an axe is Dexterity + Melee.
Attacking your fists, kicks, claws, or teeth is Dexterity + Brawl
Attacking with a ranged weapon is Dexterity + Archery or Dexterity + Athletics.
In D&D10 combat, accuracy is just as important in raw power. Damage rolls are determined by strength, if you roll better than the minimum necessary to hit, you do extra damage. If you don't roll the minimum necessary to hit, you don't get to do any damage no matter how strong you are.
Outside of combat, Dexterity is commonly tied with Crafts when a character wants to make something requires a high level of skill.
Dexterity is paired with Performance for playing a stringed or percussion instrument or dancing.
Dexterity is paired with Medicine when stitching up a wound.
Picking pockets requires Dexterity + Legerdemain, as do most fake magic tricks.
Dexterity is paired with Riding when attempting difficult tricks and staying saddle born, though Riding is often paired with many attributes.
Dexterity + Athletics is used for physical actions based on speed or agility.
Very high and very low Dexterity characters may demonstrate their agility or lack there of in their movements but it's not always possible to gage someone's Dexterity by looking at them.

When is Strength Used?

Strength is rarely rolled when paired with an ability like most other abilities. The major exception is athletics, Strength + Athletics is used to jump, swim or climb.
In some rare counterexamples you might roll Strength + Intimidation to cow someone by manhandling them or Strength + Craft to make quick crude repairs on something bulky. You might roll Strength + Animal Ken to physically rein in frightened animals. A performing troupe Strongman might roll Strength + Performance to exhibit feats of strength in a showy manner.
Usually, Brawl attacks and defense are based on Dexterity but grapples and wrestling maneuvers use Strength instead in both offense and defense.
Most commonly Strength is used to determine your base damage with a melee weapon, brawling attack or a bow.
Strong characters can carry more gear and wear heavier armors. Some weapons have a minimum strength rating.
A character's Strength rating is used as a baseline for Feats of Strength which lets a characters due mighty feats in short bursts such as knocking down doors or flexing out of ropes and chains.
It is fairly common to have opposed strength rolls as characters fight over items both have a grip on or one character tries to kick open a door the other is bracing. Strength is also used to resist unorthodox restraints such as magically constricting vines.
With a few exceptions, characters with high Strength tend to be bulkier, so characters can often a gage another's strength with a casual look unless they are wearing baggy clothing.

When is Stamina Used?

Stamina is rarely rolled when paired with another attribute. The exception is if you have to do something marathon style. If you need to do forced marching you may to roll Stamina + Athletics or Stamina + Ride. Sailors might have to roll Stamina + Sailing if they have to keep pushing on without adequate sleep.
If you have to pull an all-nighter to comb through hundreds of books in a dusty library to look for one elusive answer you may have to roll Stamina + Alchemy or History or whatever thing you are researching. You might have to roll Stamina + Craft or Engineering to complete some critical project working through the night.
More commonly Stamina is rolled by itself to resist Fatigue, soak bashing damage, resist poison or resist magical attacks that impact the body.
If a character is wounded, I usually make him or her make a reflexive Stamina check to keep their footing and/or avoid dropping what they are carrying.
It is hard to gage a person's Stamina by looking at them, but to some extant you can gage a person's Stamina by how they carry them selves.

When is Perception used?

Perception isn't paired with many things often but the rolls they are used in are often critical.
Passively noticing things, be they subtle clues to the next story hook or the thug sneaking up on you, roll Perception + Alertness.  Outside of combat, Perception + Alertness seems to be the most common thing I ask people to roll.
Actively searching for things normally uses Perception + Investigation.  
Reading hidden emotions and trying to smell out lies uses Perception + Empathy.
Tracking in the wilderness involves Perception + Survival.
The above rolls are pretty common but less commonly Perception can be used for specific professional judgments.  Perception + Commerce for appraising merchandise, Perception + Ride for appraising horses, Perception + Crafts for perceiving the quality of workmanship, Perception + Melee for watching a tournament to gage a potential opponents' or allies' strengths and weaknesses for later.

When is Intelligence used?

More often than not, Intelligence is rolled to see if your character can recall a useful fact when the fact might be relevant.  Intelligence is especially commonly paired with Rare skills.
Who's heraldry is that? Who are that groups allies and rivals. Roll + Intelligence + Politics, to see how much your characters knows.
What poison does this look like, and do I know the antidote?  Roll Intelligence + Hearth Wisdom.
What are the beliefs of the clergy wearing that particular symbol?  Roll Intelligence + Theology.
What is the weakness of a kappa?  Roll Intelligence + Arcana?
What spell could cause this effect?  Roll Intelligence + Spellcraft?

Intelligence is also used to work out problems when you have time to think things over.  Essentially making educated guesses.
(Over a map) The bandits have struck here, here, and here.  Their next attack is likely to be in ______ region.  Roll Intelligence + Investigation.
(over a map) the dragon was sighted here, here, and here. Where is it probably lairing? Roll Intelligence + Survival.
The best reagents in the forest are probably in what area?  Roll Intelligence + Hearth Wisdom. 
This puzzle box unlocks the door.  Roll Intelligence + Enigmas to solve the puzzle box.
Based on the recent inclement weather, the local game is probably huddled up here.  Roll Intelligence + Survival.
I need to find a discrepancy to prove that the king's steward is embezzling funds.  Roll Intelligence + Seneschal.

How Social Attributes Work?

Compared to physical actions, and especially combat, social interactions are often more improvisational for both the players and Game Master.
Usually Charisma is used if you are trying to socially persuade someone honestly and Manipulation is used for less honest or coercive actions.
Appearance can be swapped for Manipulation or Charisma with any social interaction based on first impressions. If a character is trying to seduce another or using flirtation and attraction to enhance a social attempt to persuade or trick someone, Appearance can and usually should be swapped for Charisma.
Appearance is often unrolled. Often NPCs just reflexively treat high Appearance characters nicer than low Appearance characters. This bias is still in play even when the characters are not sexually attracted to them. Though if a character is trying to blend into a crowd, a high Appearance becomes a liability though a character can try to mitigate this by dressing down.

Emotional appeals usually use Empathy which can be paired with almost any social attribute. Appearance + Empathy is used to get an audience as a stranger or lay the ground work for flirtation. Charisma + Empathy can build trust and comradery while Manipulation + Empathy can ferret what buttons to push to use someone's emotions against them.
Getting someone to believe a lie usually involves Manipulation + Subterfuge but convincing someone that your idea is actually their idea might involve Charisma + Subterfuge.
While Investigation can be paired with many attributes, in most investigations, the core of investigation is asking the right people the right questions. Charisma + Investigation is for talking to people who are neutral or on your side, Manipulation + Investigation is for talking to people who are somewhat hostile to you or your end goal. Appearance can be used if flirtation is involved or if you are a true stranger trying to find helpful information in a new area.
Leadership is a mixed bag. If you want to inspire courage and loyalty, Leadership is usually paired with Charisma. If you want to make sure that the three squads you are commanding coordinate their separate actions at exactly the right time according to your plan, roll Manipulation + Leadership. Appearance might paired with Leadership if you are trying to make a grand entrance.
Etiquette is usually paired with Charisma or Appearance to make a good impression with individuals or groups but you are not looking for anything specific. Manipulation + Etiquette might be used if the situation calls for heavy subtext and air of plausible deniability.

Wits, the redheaded stepchild of the attributes

Wits is probably the least mechanically useful attribute in D&10. It is technically a mental attribute, but Wits ha an identity issue and sneaks into other category often.
In combat you might have to roll Wits + Something to reflexively to abort and/or change what you were doing if circumstances change rapidly in unexpected. Perhaps the particular enemy you were about to strike has fallen and you want to strike someone else or perhaps a non-combatant is now in the line of fire. If you want to not just abort your action, but change it to something more useful, makes a straight Wits roll.
If your horse suddenly bucks or is shot out from under you, you need to roll Wits + Ride to avoid being thrown into the dirt. Wits + Animal Ken can help a character avoid being bitten or kicked by a frightened animal.
If a social interaction depends on rapid improvisation instead of a pre-developed plan or familiar social norms, than Wits can and probably should be substituted for a social attribute.
If you want to maintain a "poker face" when happy, scared, sad or surprised you usually have to roll Wits + Subterfuge or Wits + Performance.
Most deceptions involve Manipulation + Subterfuge, but if you are trying to fast talk a target than Wits + Subterfuge is used instead.
It is uncommon, but Wits is used to resist some magical attacks.