Prohibited (signs and rules): cấm, không + verb

Cấm means "forbid", and you'll see it most on signs, straight before a verb: Cấm hút thuốc (no smoking), Cấm đậu xe (no parking; in Hà Nội, Cấm đỗ xe). It's short and strong, the language of rules.

Signs also use plain không before the verb, which is a little softer: Không hút thuốc. Polite notices in hotels and shops start with vui lòng (please): Vui lòng không hút thuốc. On official notices, nghiêm cấm means "strictly prohibited".

In speech, cấm tells someone what the rule is: Ở đây cấm chụp hình nha anh. You can't take photos here. When a person does the forbidding, they come first and the one forbidden goes after cấm: Mẹ cấm tụi nhỏ ăn kẹo. Mum doesn't let the kids eat sweets. People often add không được before the verb as well. It looks like a double "no", but it means the same: Bác sĩ cấm ba không được hút thuốc nữa.

Cấm sounds like authority, so don't use it to ask a friend not to do something. For that, say đừng: Anh đừng hút thuốc nha. To state a rule to someone yourself, không được is the everyday choice: Em không được hút thuốc ở đây.