Everything worth knowing, nothing that isn't.
Recognize the keywords
Support STOP, UNSUBSCRIBE, and their localized equivalents on your two-way number, and process them automatically through your inbound webhook. See /answers/what-is-two-way-messaging and /answers/what-is-a-messaging-webhook.
Suppress permanently
Add opted-out numbers to a do-not-contact list checked before every send, so the number never receives another marketing message unless the user explicitly re-subscribes. See /answers/what-is-dnc.
Confirm once, then stop
Send a single confirmation of the opt-out, then nothing further — continuing to message after STOP is a violation and a trust breach. Keep an auditable record of the request and the date.
Separate transactional messages
Essential transactional messages (like security alerts) are generally distinct from marketing opt-outs, but keep the categories clearly separated and never use a transactional channel to slip in marketing. See /answers/sms-compliance-checklist.