Edge of the Empire is different than most systems, being more abstract while still lending itself to being a bit more of a narrative game with its fancy dice and strange symbols. Hopefully this will help clear some things up.

First, required reading: Introduction to EOTE PDF Dropbox Link: Basic of EotE

This will show how to build dice pools. Difficulties will be assigned by the GM hopefully before the roll is even considered. I will do my best to keep the flow of gameplay smooth and not let mechanics bog everything down.

Dice Recap:
Ability Die
Proficiency Die
Difficulty Die
Challenge Die
Boost Die
Setback Die

Skill ranks are abstract, so here are some clarifies that should help clear up what they represent. (Thanks to Amanda for helping me clear this up.)
0 ranks in a skill is everyday level of competence and no training.
1 rank is casual level of skill - perhaps a hobby.
2 ranks is professionally trained in a skill.
3 or more ranks in a skill represents exceptional training and aptitude with a skill.


Making the Roll

Each skill is directly tied to an attribute, from Astrogation to Xenology. That determines your dice pool. First, to clear up some nomenclature:
"Upgrading ability dice" represents removing a green Ability die and replacing it with a yellow Proficiency die. If all the dice in the pool are already Proficiency dice, instead add a green Ability die to the pool. If there are still upgrades left, upgrade that Ability die to a Proficiency die. Repeat as necessary.
"Upgrading difficulty dice" represents removing a purple Difficulty die and replacing it with a red Challenge die. if all dice in teh pool are already Challenge dice, instead add a purple Difficulty die to the pool. If there are still upgrades left, upgrade that Difficulty die to a Challenge die. Repeat as necessary.
"Downgrading dice" is a specific mechanic and applies only to yellow Proficiency and red Challenge dice. When they are downgraded, replace a number of dice equal to the downgrade amount with their lower version (green Ability dice or purple Difficulty dice, respectively). If there are downgrades left but no dice of that type left to downgrade, further downgrades are ignored.

Step 1: Applying Skills and Characteristics
Pick the skill you want to use for a roll and find the relevant characteristic. Pick the higher of the two, and gather that many Ability dice. Then, upgrade a number of times equal to the lower of the two.
Example: Kred has an Agility of 3 and a Ranged (Light) of 2. He gathered 3 Ability dice (equal to his Agility), then upgrades 2 times (equal to his Ranged (Light)). This leaves him with a pool of 2 Proficiency Dice and 1 Ability Die ().

Step 2: Applying Task Difficulty
The difficulty is set by the difficulty of the task. See the table below for examples. These difficulty dice are then added to your dice pool with your dice from the previous step.
Example: Kred is trying to shoot a target at Close range, which is a Easy (1 Difficulty die). He adds 1 purple Difficulty die to his pool, giving him a total pool of 2 Proficiency Dice, 1 Ability Die, and 1 Difficulty Die ().

Difficulty LevelDiceExample
Simple-Routine, with the outcome rarely in question. Usually not rolled unless the GM wishes to know the possible magnitude of success, or Setback dice indicate the possibility of complications.
EasyPicking a primitive lock, tending to minor cuts and bruises, finding food and shelter on a lush planet, shooting a target at close range.
AveragePicking a typical lock, stitching up a small wound, finding food and shelter on a temperate planet, shooting a target at medium range or trying to strike a target while engaged.
HardPicking a complicated lock, setting broken bones or suturing large wounds, finding food and shelter on a rugged planet, shooting a target at long range.
DauntingPicking an exceptionally sophisticated lock, performing surgery or grafting implants, finding food and shelter on a barren desert planet, shooting a target at extreme range.
FormidablePicking a lock with no comprehensible mechanism, cloning a new body, finding food and shelter on a planet without breathable atmosphere.

Step 3: Modifying the Pool
Further modifications to the dice pool are made here, including blue Boost dice and black Setback dice. These represent minor advantages and equipment. A Boost die, for example, represents a useful piece of gear or the element of surprise. A Setback die represents a minor disadvantage to the roll, such as poor lighting or inferior supplies. These dice do not cancel each other out. You may have multiple dice of each type added to the roll.
In addition, this is the step where dice are upgraded or downgraded. Special talents, actions, and situations upgrade and downgrade dice appropriately.
Some dice may also be removed due to special talents and equipment. This is done after all other dice have been added, and all upgrades and downgrades have been applied.

Example: The target Kred is trying to shoot is in poor Lighting, adding a black Setback die, but he has the element of surprise, adding a blue Boost die. This makes his final dice pool 2 Proficiency Dice, 1 Ability Die, 1 Difficulty Die, 1 Boost Die, and 1 Setback Die ().

Step 4: Make the Roll and Interpret it
The roll is made and interpreted, as seen in the Intro PDF. It is exactly as described there. The dice roller will handle this for you. Here is a quick recap:
Failure cancels Success.
Threat cancels Advantage.
Triumph and Despair do not cancel each other out. Each Triumph represents a success symbol that can be cancelled normally, as well as a "special effect". Each Despair represents a failure symbol that can be cancelled normally, as well as a "terrible, horrible thing". Examples of these will be added into the combat brief, but the possibilities are endless.

Opposed Checks
When a check is opposed, the active character builds a dice pool whose difficulty is based on the skills of the opposing character, treating the opposing character's skills and characteristics as Difficulty dice instead of ability dice.

Example: Kred is trying to sneak by a security patrol. Kred has an Agility of 3 and a Stealth of 1, giving him 1 yellow Proficiency die and 2 green Ability die. The patrol has a Cunning of 2 and a Perception of 1. This adds two purple Difficulty dice to the check, then upgrades 1 of them, making the final dice pool 1 yellow Proficiency die, 2 green Ability dice, 1 red Challenge die and 1 purple Difficulty die ().

Assisted Checks:
Characters may offer skills assistance if they have skill ranks in the task. When they do, they may combine their ranks in the skill and characteristics, taking whichever is higher.
Example: Pash has an Intellect of 2 and Astrogation of 3 while 41-VEX has an intellect of 3 and an Strogation of 1. The player uses Pash's Astrogation of 3 and 41-Vex's Intellect of 3, making the dice pool 3 yellow Proficiency dice ().

Unskilled Assistance:
If an assisting character is not skilled in the task, they may add a single Boost die to the check.


Destiny Points

The Destiny Pool represents the players being more than just the everyday person in the galaxy and offers some control over their Destiny. Destiny will be tracked in a topic title.
Players have access to the Light side of the Destiny pool while the GM has access to the Dark side of the Destiny Pool. Players may not spend Dark side points and GMs may not spend Light side points. When a Light side point is used it becomes a Dark side point, and vice versa.

Only one Destiny point may be spent on any single check.

Destiny Points may be used to:
Upgrade a dice pool by one step.
Upgrade the difficulty of an opposing skill check by one step.
Activate powerful special abilities and talents
Introduce new "facts" and context directly into the narrative.
 Example: Landing unexpectedly on a hostile planet with toxic air and spending a Destiny Point to suggest that rebreathers were packed at the last port.
Example: Moving through a medical facility and finding a spare stimpack, or introducing a new terrain feature to use as cover.