Follow-up is the cheapest thing in a job search and the most commonly skipped.
After applying
Wait five working days. Send four lines: the role, the date you applied, one sentence on the most relevant thing you have done, and a direct question about the timeline. No apology, no paragraph about your passion.
After an interview
Send it the same day. Reference one specific thing discussed and add the detail you wish you had given. This is the only follow-up that regularly changes an outcome.
After a rejection
Ask one question: what would have made the difference? Roughly one in four people answer, and that answer is worth more than another ten applications.
How often
Two follow-ups per application. After that, move on and keep the pipeline full.