Basic d20 Premise
The basic idea of the d20 system is to assign a difficulty to a specific task and then roll a 20-sided die and add any modifiers. If the die roll plus the modifiers meets or exceeds the required difficulty, then the character successfully performs the task. If the roll is less than required, then the character fails. Exceptions are a natural roll of 1 or 20 (before modifiers are added). A natural 1 always fails while a natural 20 always succeeds. This way, there's a 5% chance for a Jedi Master to make a mistake as well as a 5% chance for the lowliest character to happen to hit a rancor directly in the eye and kill it.
Rolls are always used in combat and used at other times at the GM's (Game Master's) diescretion. I tend to use them to add an element of randomness to the game and story.
Here's an example. Han Solo wants to pilot the Millenium Falcon through a closing shield door. This is a very difficult maneuver, so it is given a DC of 20. Han has 13 ranks in his Pilot skill, a Dex of 14, and the Skill Emphasis (Pilot) feat (which gives him a +3 on Pilot checks). Checking the Ability score modifier table below, we see that a Dex of 14 gives Han a +2 to Pilot (because Pilot is based on the Dex ability). So the total bonus for Han's Pilot skill is:
13 (Pilot skill ranks) + 3 (Skill Emphasis (Pilot)) + 2 (Dex ability mod) = 18
Han rolls a d20 (20-sided die) and gets a 6. Normally, this is not a very good roll, but 6+18 = 24, which beats the DC of 20, so Han pilots the Falcon through the closing door successfully.
There are six basic abilities. The average score for each is 10, but as a starting character you will roll to determine your score in each (with a result between 3 and 18). The higher the score, the better. You can determine your initial character abilities by using the stat roll tool on my website. Roll until you get three different results with an average over 13. Be sure to write all these down and then pick one as the Ability scores for your character. You then pick which score will be assigned to which Ability. The abilities are:
Strength (Str) - Determines chance to-hit with melee attacks, the damage done by melee attacks (sword, club, etc.), how much weight you can carry, skills such as jump and climb.
Dexterity (Dex) - Determines to-hit for ranged attacks (blasters, thrown rocks, etc.), your defense (i.e. whether you can avoid enemy attacks), skills such as pilot, hide, move silently.
Constitution (Con) - How hardy your character is (i.e. Wound points, which is the amount of damage you can take before falling unconscious). Determines how many bonus Vitality points you gain when you level up (Vitality points are tied to using difficult abilities and avoiding taking Wound damge), and a few force-based skills.
Intelligence (Int) - A characters book learning. Determines the number of languages your character knows, how many bonus Skill points you gain when you level up (Skill points are used to purchase Skill abilities like pilot, repair, jump, hide, etc.), skills like search, repair, knowledge, and craft, and a few force-based skills. An absent-minded professor would have high Int but low Wis.
Wisdom (Wis) - A characters strength of will, intuition, and common sense. Determines skills like Listen, Spot, and Sense Motive, and some force-based skills. A simpleton with little schooling but great intuition would have high Wis and low Int.
Charisma (Cha) - Not just a character's looks, but also their ability to lead and personal magnetism. Determines skills like Bluff, Diplomacy, and Handle Animal. Also controls force-based abilities like Jedi mind tricks.
Ability scores modifier table:
There are a variety of races in the game, some of which provide various bonuses to different Abilities and additional Feats. Human is generally the easiest race to play, though playing another race tends to mix it up a little and can provide significant advantages. For instance, if all you want is to be a Soldier with high Str, Wookie is a great race. However, Wookies get penalties to Dex, Cha, and Int, so they would make terrible Nobles. Check the book for information on races.
You'll be choosing from a variety of classes of character. These basically determine your character's abilities. Here's a list of the one's you can initially choose from:
Fringer - Luke before he met Obi-Wan. Fringers are generally regarded to be a pretty weak class. However, they have high defense and would do really well on Junkyard Wars.
Noble - Princess Leia. Nobles inspire others and make great negotiators.
Scoundrel - Han Solo, Lando Calrissian. Have more skills than any other class. Soundrels operate through stealth and guile, often outside the general rules of society.
Scout - Chewbacca. Scouts can operate very well in the wilderness of space and backwater planets. Aragorn as a ranger, before he takes the mantle of King, is also a good example of a scout.
Soldier - A stormtrooper who could actually hit something. Warriors. Very good in a fight, but sometimes at a loss in other situations.
Tech Specialist - A specialist in a specific field. This could be a surgeon, starship mechanic, droid programmer, etc. Though I initially liked this class, I think it's crippled because they get very few Skill points.
There are a number of different skills in the Star Wars universe. Each skill is based on a specific Ability. You spend Skill points each time you level up to buy your character ranks in various skills.
Link to a list of skills categorized by controlling Abilities