leveling up proccess as a caster

i have never played a caster before(new and tend towards fighters)

can somoene help me understand the process of lvling properly in the case of spells.
in my current game the GM has been nice and let us u lvl just take the spells.

what is the proper way to do this?

Depends on whether or not you are a prepared or a spontaneous caster.

Prepared casters like wizards and witches add 2 spells to their spellbook/familiar every time they level for free, you can gain additional spells by paying for them and/or undergoing a special ritual.

Humans can add to this number for free by spending their favored class bonus.

Spontaneous casters have a table which lists how many spells they know. You pick that number of spells. When you level, you add the difference between the previous number and the current one for each spell level as it states on the table.

Again, humans can add to this number, but only by selecting spells below the highest spell level they can cast.

Divine casters like druids and clerics receive their spells from prayer, and it it sort of assumed that they learned all their spells through their religious training in their backstory and thus do not have any restrictions on what spells they can prepare. Divine Spontaneous casters like the oracle have a spells known list like the sorcerer.

Hope that helps you.

Keep in mind the difference between "class level" and "spell level" (poor wording inherited from early game versions). You won't have 2nd-level spells at 2nd level in a class. You usually only get higher-level spells every two or three class levels. The table for you class can show you.

so to be clear, im in the middle of a dunguen the GM says he by the way here is enough XP to lvl, and DING 2 new spells show up in my book(assuming the lvl increase gives me new spells)

Ask your GM about that. My GM has a house rule that you need to get a night's rest before you gain a level, and I know of other GMs who require more down time than that.

Mechanically that is correct, "ding 2 news spells show up in your book" but the story line behind it is your character has been studying, practicing and perfecting spells during your adventuring career and you just "got it" and now can use 2 new spells you have been practicing all along.

Back in the old days... there used to be in game training time required to level. You needed to find a mentor/trainer, spend weeks with them learning new skills, then pay them for their time before you could level up. The details were removed, but nothing was ever added to fill the gap. So now it has become a DM decision as to what makes the most sense in their campaign.

That is like any other class really.

If the GM allows you and others to lvl then everybody , not only the casters , get everything right at that moment.

Ofc , lvling atleast on the games i play , isnt a full refresh like in video games , you still need to heal to get those new HP points...

We use some "narrative houserules" as a solution for our campaign to avoid the "ding: you got new spells out from nowhere" effect:

For Wizard/Alchemist/other classes with spell books: Every day when the wizard spent 1 hours to prepare his spells he also did a small amount of researches for the new ones into the blank pages of spell book, and the first morning he got the 2 new spells after the level-up event it's because the PC was finally able to figure how to cast them.

For spellcasters with some kind of Communion with the Other (Witch, Cleric, Nature) it's easier, since your PC's ability to commune was improved by the use in the previous days, and it's even easier for the spontaneous-non commune casters where your's PC "blood/inspiration" has awaken a new power (sorcerers/bards).

If you are leveling up then you get whatever your new level says you get. Spells appearing in your spell book is no more unrealistic than suddenly learning a new feat, or being an expert at dealing with a completely different type of creature. If the ranger can gain his next favored enemy including the extra +2 for gaining a new enemy, why is it so hard to accept you gain new spells?

Part of the leveling up is the fact you are studying and training during the time between levels. Much of this is assumed to be happening in the background so there is no real game mechanics involved. For a wizard it may be that he is researching the spells he will learn when he levels up. When you finial actually gain the level something clicks and you figure out what you were missing. Your spell book may have notes in it that you are working on. The next time you prepare your spells you simply add whatever it was you missed.

Keep in mind that a prepared caster still has to prepare his new spells. So even if you just figured out the new spell you will need to prepare it. A spontaneous caster on the other hand is simply be able to cast the new spell.