Learn Dutch: De ochtend begint met het werk. - The morning begins with the work.

The full dictionary form (infinitive) of the verb is beginnen (to begin). To find the stem, we drop the -en, leaving begin. Because the subject here is de ochtend (the morning, which acts as an "it"), we follow the regular rule and add a -t to the stem: begin + -t = begint.

Why does the sentence use both de and het for "the"?

Dutch has two different words for "the": de and het. Every noun is assigned one of these, and there is no simple rule to guess them, so you have to memorize the article along with the noun. Ochtend (morning) is a de-word, while werk (work) is a het-word.

Is werk a noun or a verb in this sentence?

It is a noun here, meaning "the work". You can tell because it comes right after the word het (the). The verb form "to work" is werken.

Does met translate exactly to "with" here?

Yes! Met is the standard Dutch word for "with". Just like in English, you can say that something "begins with" (begint met) something else. It is a very straightforward translation.