[verb (dictionary form)] + べきだ [する → す] + べきだ [verb (dictionary form)] + べきではない / べきじゃない [verb (dictionary form)] + べき + [noun] [noun] / [na-adj] + であるべきだ
べきだ says what someone should do because it is right: a judgment about duty or proper behaviour, "should", "ought to". It follows the dictionary form of a verb, and with する both するべきだ and the more written すべきだ are correct. The polite form is べきです.
The verb stays in the dictionary form. To say "should not", the negative goes on べき: べきではない, or べきじゃない in speech.
べきだ is the speaker's view of what is right. A rule, a schedule or a plain necessity takes なければならない.
In the past, べきだった is "should have": it wasn't done, and that was a mistake. べきではなかった is "shouldn't have".
These go beyond a verb + べきだ at the end of a sentence.
べき goes straight before a noun, with no だ: "a thing to be done", "a book to read".
A noun or a な-adjective takes である before べき. This belongs to writing and formal speech.
A few verbs + べき work as adjectives with no sense of duty: おどろく驚くべき "astonishing", おそる恐るべき "formidable".