Learn Dutch: Ik vind dat we moeten samenwerken. - I think that we must work together.

The word dat (that) is a subordinating conjunction. It introduces a dependent clause and forces all the verbs in that clause to be pushed to the very end of the sentence.

When there are two verbs at the end like this, how do I know which one goes first?

In a sub-clause, the conjugated verb (the one that changes to match the subject, which is moeten here) generally goes right before the infinitive verb (the full dictionary form, here samenwerken).

Why does the sentence use vind instead of denk for "think"?

In Dutch, vinden (literally "to find") is the standard verb to use when expressing a personal opinion, similar to saying "I feel" or "I believe" in English. You use denken for the actual mental process of thinking. Since this sentence is sharing an opinion, vind is the natural choice.

Is samenwerken a separable verb?

Yes! If it were the only verb in a normal main clause, it would split (for example: Wij werken samen). However, because the modal verb moeten requires a full infinitive, samenwerken stays glued together as one word.