Learn Hardcore Dutch: Tom trekt zijn jas aan, want het regent buiten. - Tom puts on his coat because it is raining outside.

Dutch has separable verbs: here the base verb is aantrekken (to put on). In the present tense you conjugate the verb stem (trek-) in second position and move the prefix aan to the end of its clause. That’s why you get Tom trekt zijn jas aan rather than Tom aantrekt zijn jas.

Why is zijn used before jas, and how would I translate it?

Zijn is the masculine singular possessive pronoun “his.” We use it because Tom is male. So zijn jas literally means “his coat.” (Informally you might see z’n jas, but zijn is the full form.)

What does want mean, and how is it different from omdat in terms of word order?

Want is a coordinating conjunction meaning “because,” joining two main clauses. With want you keep the normal Dutch main-clause word order (subject–verb–object), so het regent buiten stays S–V–Adv.
Omdat is a subordinating conjunction. If you replace want with omdat, the verb moves to the end:
“Tom trekt zijn jas aan omdat het buiten regent.”

Why is buiten placed at the end of the sentence?

Buiten is an adverb of place (“outside”). In Dutch main clauses, adverbs of time, manner and place typically follow the finite verb (and any objects), so they land at or near the end:
“Tom trekt zijn jas aan, want het regent buiten.”
You could front it for emphasis (“Buiten regent het”), but in normal explanation of cause it stays at the end.

Is the comma before want necessary, and what are the punctuation rules?

When you join two independent clauses with want, Dutch style strongly recommends a comma before want to signal the clause break. It isn’t strictly mandatory in very short sentences, but it makes your writing clearer and more correct.