Start with the timeline you were given
Send a thank-you within a day. If they named a decision date, wait until the next business day before asking for an update. If no timeline was given, five business days is usually a measured first check-in.
Make the message useful, not merely visible
Mention the role and interview date, thank them, then connect one need discussed in the interview with a specific way you could help. Ask whether they need anything else rather than demanding a decision.
Know when the follow-up is final
One later note is reasonable if the revised date also passes. After that, keep applying elsewhere. Repeated messages do not create a vacancy or speed an internal process.