How do you determine the Spellcasting ability and the spell attack bonus? I've tried searching for it in the player's handbook and searched for answers here, but I haven't found anything.
Page 114 of the player's handbook under the Spellcasting Ability header lists the ability and relevant spell modifiers for wizards:
Intelligence is your spellcasting ability for your wizard spells...You use your intelligence whenever a spell refers to your spellcasting ability:
Spell save DC = 8 + your proficiency bonus + your Intelligence modifier
Spell attack modifier = your proficiency bonus + your Intelligence modifier
Note that the same rules can be found on page 32 of the basic rules
The spellcasting ability is Intelligence.
The proficiency bonus is in the Wizard table of PHB p113.
Your Spell save DC equals 8 + proficiency bonus + Intelligence modifier.
Your Spell attack modifier equals proficiency bonus + Intelligence modifier.