The "skill attack modifier" applies to the following skill uses:
Deception
- create a diversion to hide
- convey deceptive information
Persuasion
- improve an NPC's attitude
- intimidate an NPC
Use the Force
- use Force powers
- use some Force talents
To determine someone's skill attack modifier, use the following formula:
character level + ability modifier + miscellaneous modifiers
Character level: They get to add their full character level to the modifier (which is essentially like giving them full BAB with a weapon), but they do not get to add +5 for being trained or for having Skill Focus.
Ability modifier: This is always going to be Charisma, but it's probably a good idea to leave it open anyway. For instance, I have a player who took a talent called Fade Out (Galaxy of Intrigue) that lets him substitute his Stealth modifier for his Deception modifier when creating a diversion to hide, so in that instance, he's using his Dex modifier instead of his Charisma modifier.
Miscellaneous modifiers: These include a -5 penalty for not being trained in the skill (just like you take a -5 penalty for not being proficient with a particular weapon) and a +2 bonus for having Skill Focus in the skill (this makes Skill Focus more like Weapon Focus, but it provides a higher benefit because there aren't as many things that you can add to a skill modifier as there are with weapon modifiers). There are a few other modifiers that you could probably add in here, but they'll be dependent on a specific feat or talent or something and I haven't had time to go through every single one of them. Generally, though, an ability that adds a bonus to a skill would add a smaller bonus to the skill attack modifier.
NB. This skill attack modifier does not replace the regular skill modifier. It's in addition to it. So when you are using a Force power, you would make one attack roll, add your Use the Force skill attack modifier, and compare it to the relevant defense score of your target. If you hit, then you take the same roll result but add your regular Use the Force skill check modifier to determine the Force power's effect.
To give you an idea of how this works, let's say we have a Jedi with Skill Focus (Use the Force) and Charisma 16 (+3). We'll assume that he doesn't ever increase his Charisma score as he levels up.
At 1st level, his regular skill check modifier is going to be +13 (5 [trained] + 5 [skill focus] + 3 [ability modifier] + 0 [half level]). His skill attack modifier would only be +6 (1 [full level] + 3 [ability modifier] + 2 [skill focus]).
At 5th level, his skill check would be +15, whereas his skill attack would be +10.
At 10th level, these would be +18 and +15 respectively.
At 15th level, these would be +20 and +20 respectively.
At 20th level, these would be +23 and +25 respectively.
So the regular skill check starts out quite high at 1st, but doesn't get a whole lot higher by 20th level, while defense scores will have far outstripped it, meaning that a Force user is proportionately more powerful at low level than at high level. That doesn't make a lot of sense. However, with the skill attack modifier, it starts out fairly low (but comparable to an attack modifier for a conventional weapon) and progresses to the point where it's actually slightly higher by 20th level, thus making it so the Force user starts out proportionately weak at low level and becomes proportionately more powerful at high level.