Is gustar a regular verb in Spanish? How is it conjugated?
Gustar, or to "like", is in fact a regular verb.
As for the conjugation of gustar, I'll post a link at the bottom of this answer to a remarkably helpful website rather than typing the whole list of conjugations (because I can't format them properly [that would be a train wreck] and it would be pretty time consuming [there are 19 tenses in Spanish —no teacher will require you to know all of them until at least your third year of Spanish]).
Gustar cannot be reflexive (never ever), meaning that the subject and verb cannot refer to the same thing so there are (only
A quick aside on reflexive verbs, though in English I might say something, jokingly, to a friend like:
I like myself.
. . . and translate it like any verb that can take on a reflexive form to: me gustarme, the actual grammatically correct version is: Me gusta a mí mismo.
Without further ado here's the link: