Finding the hole and checking the tire for whatever caused it
Okay. Tire's off the rim, tube's out. Now comes the part everybody wants to skip, and it's low key the part that saves you from doing this whole thing again tomorrow.
Here's the thing. Fixing the leak is easy. Finding out why you got a leak is the actual job. Skip that step and you patch the tube, put it back on, and get a flat in the same spot next week because there's a thorn tip or a sliver of glass still sitting in the tire waiting for round two.
Find the hole first
Pump a little air into the tube, just by hand or a few strokes of the pump, enough that it holds shape. Then bring it close to your face and listen. Slowly rotate the tube past your ear or your cheek. You're feeling for a hiss of air on your skin more than you're hearing it, honestly, especially if you've got any hearing loss from being around tools your whole life like I do.
If you can't find it that way, the bathtub or a bucket of water works fine. Dunk sections of the tube under and watch for bubbles. You don't need a tub full, just enough water to submerge a few inches at a time.
Once you find it, mark it. Crayon, chalk, a pen if that's what's in the drawer. I use a piece of tape folded over the tube like a little flag. Don't trust your memory here. You will lose track of exactly where it was in about ninety seconds, I promise you.
Now check the tire, not just the tube
This is the step people blow past. The tube tells you roughly where on the wheel the problem happened. The tire is where the actual culprit usually still is.
Take your marked spot on the tube and match it up to the same spot on the tire, matching valve stem to valve stem so your orientation's right. Then run your fingers slowly along the inside of the tire at that spot. Slowly. Not a quick swipe.
Real caution here: do this carefully. If there's a sliver of glass or a wire poking through, you can slice your finger open just from moving too fast across it. I tell people to go slow like you're checking for a splinter in the dark, because that's basically what it is.
If you find something, pull it out with your fingers if you can, or needle-nose pliers if it's stubborn. Then check the outside of the tire too, tread and sidewall, for cuts, embedded glass, anything that looks like it doesn't belong. Sometimes the thing that caused the flat already worked its way out and all that's left is a tiny slit in the rubber. That's fine, you just want to know it's not still in there.
If you don't find anything
Sometimes there's nothing. Pinch flat, old tube finally giving out, rim tape that shifted and left a spoke hole exposed. That's all normal. Check your rim tape while you're in there, actually, run a finger around the inside of the rim itself. If you feel a spoke nipple poking through or the tape's slid to one side, that'll cause a flat with zero drama, no glass required.
This is a little like the first time I trued a wheel. I didn't have a stand, I zip-tied a piece of wire to the fork as a fixed point and spun the wheel to see where it wobbled against it. Took me an hour, wasn't a perfect job, but it told me exactly where the problem was instead of me guessing. Checking a tire for the cause of a flat is the same idea. You're not fixing anything yet. You're just figuring out where to look.
Don't skip this and air it back up blind
I'll be honest, the very first flat I ever fixed, for the kids, I skipped this whole step. Popped the tube in, aired it up without checking a thing. It went flat again in the driveway before I even got the wheel back on the bike, thirty seconds, tops. Turned out I'd pinched the new tube with the tire lever putting it back in. Jackson thought it was the funniest thing he'd seen all week, and honestly he wasn't wrong to laugh. That's what happens when you rush the check.
So. Find the hole, mark it, run your fingers slow around the inside of the tire at that spot, check the rim tape while you're at it. That'll get you most of the way to actually solving this instead of just delaying it.
Before next time: if you've got an old tube lying around, practice finding a hole on it with the water method, even if you already know where it is. Getting fast at that step makes the real ones a lot less annoying.