Burn is an ambiregular verb - it has the third person form "burns", the -ing form "burning", and a regular preterite and past participle "burned", but also has an alternative irregular preterite and past participle "burnt". The regular form is particularly used in American English; the irregular form is moreso used in British English. In this regard, it is similar to other verbs ending in /ɜ:(r)n/, i.e. earn and learn.
Burn is an ergative verb; if used intransitively, the subject is damaged by fire; if used transitively, it is the object that is damaged by fire. Burn can also be used reflexively, e.g. "I burnt myself whilst cooking".
Note the phrasal verb "burn down" which means burn completely.
Speakers with non-rhotic accents don't habitually pronounce the /r/ sound in this burn but lengthen the vowel instead.
Students may try to use "fire" as a verb meaning burn, e.g. *"the house fired", but fire cannot be used as a verb with this meaning.