"Vai a dormire", assuming it's an order, else you "just" have to conjugate the verb andare (to go) then add "a dormire". Take note that andare is an irregular, polythemathic verb.
"Vado a dormire" is an Italian equivalent of "I'm going to sleep."Specifically, the verb "vado" means "(I) am doing, do go, go." The dependent preposition "a" means "to." The infinitive "dormire"...