Depends on the class, class level and attributes that influence the casting class.
For which class?
Still need to know the class and attributes...
Look at the table associated with whichever class you are interested in, specifically 'Spells Per Day' and then check your casting attribute to see if there are any bonus spells to adjust the table with. You may only prepare spells of a level you can actually cast (if your bonus spells grant you a second level spell, you could not prepare/cast it until your class allows you 2nd level spells).
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Each class that prepares spells is different. These differences are clearly illustrated in the table for each class - such as table 3-16 (page 80 of the CRB) which shows that a level 1 Wizard can prepare 3 0 level spells and 1 1st level spell.
In addition, the player needs to reference table 1-3 (CRB page 17) which enumerates how many bonus spells a character can prepare due to high ability scores. For instance, our first level wizard friend above has, for the sake of example, an 18 Int. The chart indicates that he would receive an additional or "Bonus" 1st level spell. He'd also have bonus slots for 2nd, 3rd, and 4th level spells, but would not yet be able to access those slots, as he cannot yet cast spells of those levels.
Finally, if our hypothetical wizard were a specialist, he would get to prepare an additional spell of his specialty school, as described on the top left of page 79 of the CRB.
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I'd like to know the amount of spells all the classes that can spellcast can prepare at level 1. I would especially like to know how many spells a level 1 wizard can prepare.
To my knowledge, there is no "master chart" that lists the number of spells that can be prepared by every class and level. Someone may have compiled such a thing somewhere on the internets, but there is no official product that does this. I've always simply thumbed through the class descriptions.
My question is how did he get the seventh spell?
If you speak about his spellbook, a wizard knows all cantrips (except from opposed schools) and 3+INT mod 1st level spell at level 1 (so 3 + 4 [INT] = 7 spells of level one into his spellbook).
This :
This wizard can prepare 3 cantrips and 1 level one spell. He has a high Int. so he gets on extra level one spell. He also specializes in a school so he gets a bonus spell from that school as well.
refers to his slots (you can find them into his special attacks).
If you specialize do you get a bonus cantrip?
I would have said that you don't, but the sheet you quoted got one in bonus... I wonder.
