With the tire off, go around it, squeezing the tread area with your thumbs. Usually you'll see a cut or some damage. Inspect the cut for a bit of glass or rock. Usually you can flick it out with the point of a knife, but be careful not to do more damage to the tire. Then look on the inside of the tire to see if it came through at all. That might be your problem.

To find the leak in a tube, blow it up until it's pretty big. For an ordinary road tube, until it's about 1.5" in diameter. Then go around it, spinning the tube with your mouth open and the tube between your lips. Usually you'll feel the leak with your lips. If that doesn't work, immerse part of the tube in a sink full of water. Go around, spinning the tube in your hands, and wiping off bubbles that stick to the tube. You'll eventually see a stream of bubbles.

The other thing to check is, once you've found the leak, if the leak is on the inside of the tube. If that's the case, there's a problem with your rim tape. A bit of metal could be poking through the rim tape and puncturing the tube.

In 60 years, I've never had a flat from getting a bit of dirt in the tire while changing a flat. I suppose it's possible, though.

Another possibility is a bad valve. Rare, though. Very common to have a leak at the base of the valve stem, where it's joined to the tube. If so, toss it.