Basically just the title. Is it constantly six or does it increase when you level?

The number of spells that a wizard can prepare is your intelligence modifier plus your level. The number of spells in your spell book starts at 6 and you can find more plus you learn 2 more each time you level. Wizards always have more spells in their spell books than they’re able to prepare. 

Quote from Brian_Avery >>

To add to what Tim said, you also only get two 1st level spell slots, which means although you have 6 spells in your book, and have prepared maybe 4, you can only cast 2 with spell slots. (This is a good reason to have a few Ritual spells, if you cast them as a ritual you don't need spell slots... go wizards!)

 And for making spell scrolls

Quote from Tim >>

The number of spells that a wizard can prepare is your intelligence modifier plus your level. The number of spells in your spell book starts at 6 and you can find more plus you learn 2 more each time you level. Wizards always have more spells in their spell books than they’re able to prepare. 

 I have found the last part of your answer to be wrong, while Multiclassing as an Owlin Rogue(3)/Wizard(2). I have five spells with three Cantrips, and my Int modifier is +3, so with the rules you have stated, I can actually prepare all five of my spells (but only have three spell slots to use them.) And oddly, I found that I only started off with the ability to learn five spells.

Quote from Soupdup89 >>

Quote from Tim >>

The number of spells that a wizard can prepare is your intelligence modifier plus your level. The number of spells in your spell book starts at 6 and you can find more plus you learn 2 more each time you level. Wizards always have more spells in their spell books than they’re able to prepare. 

 I have found the last part of your answer to be wrong, while Multiclassing as an Owlin Rogue(3)/Wizard(2). I have five spells with three Cantrips, and my Int modifier is +3, so with the rules you have stated, I can actually prepare all five of my spells (but only have three spell slots to use them.) And oddly, I found that I only started off with the ability to learn five spells.

 
Multiclassing only affects the number of spell slots you have, if you have more than one class that uses spell slots.

Otherwise you gain and prepare spells the same way individually. As a 2nd level Wizard, no matter your multiclassing, you would have 8 spells of 1st level, 3 cantrips and can prep 2 + int mod (in your case, 5).