How do you say continue in spanish?

"Continued" is a verb, so you would need to conjugate in accordance with the subject. The verb is continuar and is a normal "ar verb" in the preterite and imperfect tenses.

Preterite: continué, continuaste, continuó, continuamos, continuasteis, continuaron

Imperfect: continuaba, continuabas, continuaba, continuábamos, continuabais, continuaban

If you want the past participle "continued", e.g. I have continued to talk to him. It would be: continuado.

If you want to use the phrase "to be continued", the expression in Spanish is "a continuar"