To determine what reagent you need, it might be helpful to look up your spell here. It will tell you.
Many reagents are gems. These are purchasable at many vendors that sell gems or Caster supplies.
Some of the LDoN spells require scrying stones available at the Magi.
Bone chips are dropped, reagent for Necro/SK pets.
Tiny Daggers for Enchanters are at Caster Suppliers likely listed as General Merchants.
Reagents for removing augments are available in your guild hall, or in the Butcherblock Adventure camp, probably Abysmal Sea too.
If you are a druid and want to cast a fire-based spell you need a fire beetle eye (dropped).
That's most of the basics...