Learn Dutch: Hij is blij als wij de nieuwe jas ophangen. - He is happy when we hang up the new coat.

The word als introduces a subordinate clause. In a normal main clause, you split separable verbs (like wij hangen de jas op). But in a subordinate clause, the verb is pushed to the end of the sentence and snaps back together into a single word: ophangen.

Why does nieuw have an -e at the end (nieuwe)?

Because it describes the noun jas, which is a de-word (de jas). Adjectives usually get an -e ending when they come right before the noun. The main exception is when you describe a het-word using een (a/an) or no article at all.

Does als mean 'when' or 'if' here?

It can mean both! Dutch uses als for both 'if' and 'when' in the present and future tenses. You have to rely on context to decide which one makes more sense in English.

Could I use we instead of wij in this sentence?

Yes, absolutely. Wij puts a slight emphasis on 'we' (meaning we are hanging it up, not someone else). If you just want to state the fact without any special emphasis, the unstressed form we is perfectly fine and very common.