I just started playing pathfinder and I've never played a game like this before. Do I have to erase and rewrite all of the numbers on my character sheet every time I level up? I feel like the beginner book is full of things without explanation. I have played through the storyline provided in the Game Masters Guide four times and I have no idea how to properly level up our characters or where to go from there.
When you level up, select the class you want to level into - an existing class or a new one. Add the abilities you gain from the class to your sheet.
The only things you should need to erase would be your BAB, CMD, CMB, Saves, Skills, and total Hit Points - an only if they are effected by your new level. For example, if your new class/level doesn't increase your Base Attack Bonus (BAB), then your BAB won't change.
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Typically, when you level many of your stats will change. Skills, HP, BAB, saves, stats (str, dex, con, etc.), and spells are the most common to change, but many stats will be altered and some will cascade to others (e.g., BAB affects cmb, cmd, and weapon attack bonuses). This is good though as it typically represents your character becoming more powerful. Higher BAB means it is easier to hit and harder to be targeted by combat maneuvers of opponents (e.g., trip).
I have not read the beginners box, but it is intended to give you an initial taste of how the game plays and may omit things for sake of simplicity. If you have completed these and are looking for further rules relating to building characters and running games, then I recommend picking up the Core RuleBook(CRB) and the Bestiary 1.
As for where to go from here...everywhere, anywhere, or nowhere. The core assumption of the game is that the DM sets up a world and players tell the story through their actions. The DM may setup a nefarious villain who intends to conquer the tristate area, but it is up to the players to impact the world and tell their story. Will they defeat the foe, join him, convince him to join them!?! The rules simply present a basis for adjudicating interactions in the world. For example, when you try to hit the enemy roll an attack and compare to their AC to determine if you hit. Who you are trying to hit, why you want to hit them, where you are while hitting them, and what happens next is all determined by the people playing the game, which includes the DM!
These are all my opinions and experiences feel free to tell me that I am wrong (we are on the internet after all).
Nate - basically, yes.
For example, you're a level 1 fighter with the following stats:
Strength - 18
Dexterity - 13
Constitution - 16
Intelligence - 10
Wisdom - 12
Charisma - 8
Hitpoints - 13 (10 from being a fighter, 3 from constitution bonus)
AC - 15 (10 base, 3 armor, 1 shield, 1 dexterity bonus)
Base Attack Bonus - +1 (from first level fighter)
Fortitude Save - 4 (2 constitution bonus, 2 from first level fighter)
Reflex Save - 1 (1 dexterity bonus, 0 from first level fighter)
Will Save - 1 (1 wisdom bonus, 0 from first level fighter)
Skill Points - 2 (2 from being a fighter, 0 from intelligence bonus)
You hit level 2 and decide to be a fighter again.
Your ability scores all stay the same. They only go up every 4 levels, and only one ability score (for example, the 18 strength and not the +4 strength bonus)) may go up 1 point.
Hitpoints go up 1d10 + constitution bonus because you are a fighter and your hit die is a 1d10.
AC remains the same because it only goes up with improved dexterity, better armor, nicer shield, or from feats and other magic items.
Saves and base attack bonus go up according to the difference between the fighter level 1 and fighter level 2 rows of their table. For example, level 1 fighter has a BAB of +1 and level 2 fighter has a BAB of +2, so our fighter here has a BAB of 2 now. Same with saves, Fortitude goes up to 5 but Reflex and Will remain 1.
Lastly, you gain 2 skill points.
A level 2 Rogue is different. They have a different hit die, they have a different level progression table, so their numbers are different but the calculation is the same. The melee attack number is still BAB + Strength. Spell Casters get more spells, but it is always "in addition to" rather than "in replacement of".
The basic rule is to use what's on the row of the class' table for your level plus the appropriate ability bonus value.
in Heros handbook every class has instruction on what to do on each level.
example for fighter:
go to page 23 there is a blue rectangle for 2nd level, you can read the following instructions:
hit points + 1d10 + con
atack bonus" + 1
fort save" + 1
BRAVERY: Write Bravery in Section F. You get a +1 bonus on all fear saves!
Every class has this rectangles with information on what to do when you level up from 1 to 5.