You need to go, or you've run out of things to say and want a clean exit.
What to say
You say: “Well, I'm going to let you go. Thanks very much for the contact. your callsign in phonetics, clear.”
"Clear" means you're done and leaving the frequency. If you're staying on the repeater listening, say "clear and monitoring" instead.
What they will say back
"Thanks your callsign, seventy-threes, their callsign clear."
If it goes sideways
If they keep talking after you've signed off, it's fine to answer once more and then repeat your closing. Nobody is offended by someone who needs to go.
Why it works this way
"73" means best regards — it's an old telegraph code that stuck. Say "seventy-three," never "seventy-threes" (though you'll hear plenty of people say it wrong). You must identify with your callsign at the end of any exchange, which is why the sign-off always includes it.
Open this in Pocket Elmer, with your callsign filled in
More things to say
- Your very first transmission — Announcing yourself on a repeater
- Calling a specific person — When you know who you want to talk to
- Having an actual conversation — The whole arc of a repeater contact, start to finish