Cooling jars and listening for the tink
Your jars are out of the canner, and this is the part nobody warns you is a whole lesson on its own. It kind of is. This is where the seal actually happens, right in front of you, on your counter, and it's one of my favorite parts of the whole process.
Getting them out
Use the jar lifter, grab each jar around the neck, lift it straight up and out. Don't tilt it. Don't grab it by the lid. Sounds obvious, but when you're tired and it's 9pm and this is your fourth batch of the day, you get sloppy with your grip, and that's how a jar goes sideways.
Set them somewhere they can sit undisturbed. A folded towel on the counter, a cutting board, whatever. Leave space between jars, an inch or two, so air gets around all sides. Don't set them on a cold counter or in a draft from the AC vent. Big temperature swings right now aren't good for the glass. A normal spot on the counter is fine.
Do not tighten the rings when you take the jars out. I know your hands want to. Leave them alone. Loose ring, leave it loose. Same conversation as the over-tightening thing, tightening now doesn't help the seal and it can mess with the lid trying to pull down. Hands off.
Now you wait
This is the part that takes patience, which, fair warning, isn't always my strong suit. 12 to 24 hours, untouched. Don't press on the lids to check them. Don't shake the jars to see if anything's moving inside. Walk away and let them do their thing.
Somewhere in that first hour or two, you'll start hearing it. A little metallic tink, almost like someone flicked a glass with a fingernail. That's the lid getting pulled down as the jar cools and the seal forms. One, then a pause, then another a few minutes later, not all at once, they pop on their own schedule.
First time this happened to me I called my sister just to describe the sound over the phone. She did not care even a little bit. I still think it's one of the best sounds in my whole kitchen. There's something satisfying about hearing proof that the thing worked without having to do a thing yourself. The jar's just handling it.
Checking the seal the next day
Once they've had their full 12 to 24 hours, check each lid. Press the center with your finger. If it doesn't flex, doesn't pop up and down, it's sealed. If it's still got give, or if it pops when you press, it didn't seal, and that jar goes in the fridge to get eaten soon, or reprocessed with a new lid if you catch it in time.
Remove the rings at this point too. You don't need them anymore, the lid is holding on its own now, and leaving rings on can trap moisture against the jar and cause rust, or worse, hide a seal failure you'd otherwise notice. Wash the rings, dry them, put them away for next time.
Labeling, or, my confession
This is also when you'll label your jars. Contents and the date, that's all you need. I use masking tape and a marker, every single time.
I say that a little sheepishly, because I actually had labels professionally designed a few years back. Nice ones, my own little logo, the whole thing. I was so proud of them. They're sitting in a drawer in my kitchen right now, still shrink wrapped, because every single time I've got jars lined up on the counter I grab the masking tape instead, it's faster and I don't want to fuss with peeling backing off fifty little stickers at 10pm. Someday I'll use the fancy ones. Probably won't.
One thing worth saying plainly
I'll say this again because it matters: don't reuse the flat lids. The ring can go in a drawer and get used fifty times, that's fine. But the flat lid is a one-time-use item. The sealing compound on the underside is only good once. People try to save the fifty cents and reuse an old lid, then wonder why the seal failed. Buy new lids every time you can. It's the cheapest insurance in the whole hobby.
Before next time
Let your jars sit their full cooling time, check every seal the next day, and get them labeled before you forget which jar is which. Trust me, "mystery jar, guess the year" is not a game you want to play in March.