[RPG] Items to increase the number of spell slots a wizard has per day

It is referencing the Ability Scores and Spellcasters section in the chapter about ability scores. In short, you get bonus spells per day, not spells known. Extra spells known tend to be rare and difficult to get, and will spell out explicitly that this is what you’re getting.

You really want to start with 18 Int, and by 5th level you should probably have a headband of intellect +2, for a total of 20 Int. Won’t help your 3rd-level spells, but it will give you another 1st-level spell and it will also help your save DCs; any spell that someone fails a save to that they otherwise would have made, is a spell you don’t have to cast again.

Smart use of your spell slots also goes a very long way. If you hit some dudes with a fireball, they take some damage. They probably aren’t dead, though, and you’ll probably end up having to hit them with another fireball. And in the meantime, they are just as dangerous to your allies as they were before, and your allies are no more effective than they were.

If, instead, you haste your allies, you double the damage the fighter or barbarian and cleric or druid do, you give a dual-wielding rogue another attack (and, hopefully, that means another Sneak Attack), and so on. This will add up to a lot more damage than a fireball, you don’t have to worry about aiming, and if the first set of hasted attacks isn’t sufficient to kill them all, your allies remain hasted for several rounds without you having to cast another spell.

Alternatively, grease and glitterdust are some phenomenally effective debuffs: grease can have enemies flat on their back, or refusing to move for fear of falling, and really lets a rogue go to town, while glitterdust blinds which, for most things at low level, means they’re basically incapable of performing as any kind of threat. Best of all, these are a 1st-level and 2nd-level spell, respectively: you can save your higher-level spell slots for fly, perhaps, for scouting or just keeping yourself out of danger.

Ultimately, these are how a wizard is powerful, not through direct-damage. Most direct-damage spells are weak. Consequently, Evocation as a school is fairly weak (and its best spells, contingency and resilient sphere, are some of the few evocations that don’t deal damage). Specialization is a very good idea, but often because it’s no big loss to ban Evocation (and Enchantment); see here for all about specializing and the best ways to do it. You’ll notice that the four spells I recommend are all Conjuration (grease and glitterdust) or Transmutation (haste and fly); that’s not a coincidence. Specializing in these very diverse schools is an excellent way to extend your day, both by giving you another spell, and also by simply having each spell count for more.

Finally, it’s worth noting that pretty soon, your basic spells per day, specialized or not, are going to get pretty large. Pretty soon, if you spend your spell slots wisely, it will be a rare day when you are actually risking running out. For now, it’s a real concern, but you can get by. If you want, though, pearls of power are the way to expand your spells per day.