How many Spanish verbs are there? And what are they?

There are at least 12,290 in Spanish (don’t worry you don’t need to know all of them).
The Manual of Verb Conjugation (Manual de la Conjugación del Verbo) lists 12,290 Spanish verbs (this is probably not an exhaustive list). That said, any attempt at a conclusive list wouldn’t really help you, it would just be over bearing and disheartening. Most Spanish speakers don’t know every verb (just like most native speakers of any language [including English] don’t know all of the verbs in their native language).
Along with the regular verbs and their relatively straightforward conjugations, there are 63 different models of irregular verb conjugation (that I know of at least) in Spanish.
Spanish, just like any other other language, is fairly extensive however no one will ever expect you to know all of the verbs or their conjugations.
I hope this helps!