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First, how exactly does one level up? Like what is the process for what goes up or not?
Page 30 has a chart for when any character, or even a monster, gains a new Feat (every odd level) or can add +1 to a specific attribute (every 4th level).
Each specific class in the Core rulebook has a similar chart (p 32 for the Barbarian, for example), from levels 1 to 20, that details if their Basic Attack Bonus goes up that level, and which Saving Throws advance for each level acquired.
Following the chart for the Barbarian, her BAB would increase from +1 to +2, and her Fortitude save from +2 to +3, but she wouldn't gain any increase in her Reflex or Will save.
What is not shown on these charts is the increases in Hit Dice or Skills, but this information is provided at the beginning of each Class write up (page 31, in the case of the Barbarian). Using the Barbarian as an example again, she has d12s for Hit Dice and Skill Ranks per Level of 4 + Int modifier. When she 'leveled up' to 2nd level, she would roll another d12 for hit points (adding her Constitution modifier), and then add 4 more ranks worth of skills (either increasing previously chosen skills to 2 ranks, or adding 1 rank to new skills that she hasn't yet learned), modifiered by her Intelligence modifier (so, if she has an Intelligence of 8, warranting a -1 modifier, she would only gain three skill points each level, while if she had an Intelligence of 12, she would have a +1 Intelligence modifier, and gain 5 skill points per level.).
Second, how are Ability score modifiers determined?
Page 16 has the point-buy option, where you have a certain pool of points (10, 15, 20 or 25 are the listed options) and spend them using the accompanying chart to determine starting attributes.
If the GM said the game was going to be a 20 point buy game, and I wanted to play that Barbarian, I might spend 10 of my 20 points giving her a 16 Strength, 5 points on a 14 Dexterity and 5 points on a 14 Constitution, leaving her with 10s in Intelligence, Wisdom and Charisma, since she would be out of points. Or I could reduce her Intelligence or Charisma to 8, and gain 2 more points to spend elsewhere, say on a 12 Wisdom.
Other options include rolling dice to randomly generate attributes, or to used a fixed array of some sort. Page 15 offers some suggestions.
Once you've generated ability scores, you then modify them by race. If my sample Barbarian is going to be human, she would gain a +2 to put anywhere, and I could raise her Strength to 18, leaving her with starting attributes of; Str 18, Dex 14, Con 14, Int 10, Wis 10, Cha 10.
If I instead wanted my Barbarian to be a Dwarf, I would instead add the Dwarven modifiers of +2 Con, +2 Wis and -2 Cha, leaving him with a Str 16, Dex 14, Con 16, Int 10, Wis 12 and Cha 8.
Are they only the bonus provided by racial or class mods? Or, is it derived from your ability score?
The bonuses are generated from the base ability score, modified by racial modifiers. So the Human Barbarian above would have a +4 Strength modifier (from her 18 Strength), and a +2 Dex and Con modifier (from her 14 Dex and 14 Con). The Dwarven example would have only a +3 Str modifier (from his 16 Str), a +2 Dex modifier (14 Dex), a +3 Con modifier (16 Con), +1 Wisdom modifier (12 Wis) and -1 Charisma modifier (8 Cha).
I am sorry, but I have a few noob questions, for a few concepts I do not understand.
First, how exactly does one level up? Like what is the process for what goes up or not?
Second, how are Ability score modifiers determined? Are they only the bonus provided by racial or class mods? Or, is it derived from your ability score?
I'm going to try to make this over-simplified. No offense intended.
A character is a collection of descriptions, statistics, abilities, and limitations. To level up, a character's 'Experience Points' statistic must be raised above a certain point. The 'Experience Points' or XP is given to a character by the Game Master. Basically the Game Master says "SoAndSo earned 400 XP". At that point, the player who is roleplaying the character adds 400 to the current XP total. If the total is above the next threshold, the character is ready to gain a level.
To gain a level, the character must select a Class to gain that level in. Usually, it will be the same class that the character started with, such as Fighter, Barbarian, or Wizard (but it doesn't have to be).
Each of the classes gain certain abilities and raise some of their statistics as levels are gained. You can see a breakdown of what is gained in the Player's Handbook. Each class listing contains a table that has a summary of the benefits that are gained for each level.
Ability Score Modifiers are calculated from your Ability Score. for ever 2 points of ability score above 10, there is a +1 bonus to the modifier. Likewise, for every 2 points below 10, there is a -1 to the modifier. Note: This is always rounded down. a 9 gives a -1 modifier, while an 11 gives a +0.
Edit: ahhh, I know I'd be ninja'd
I know the question's answered, but it should also be noted that the act or details of leveling up are frequently the topic of house rules of a specific GM.
For ability mods on the fly, I find it easiest to minus 10 and then half it. A 19 strength gives a +4 bonus. 19 - 10 / 2 = 4.5. Round down to 4.