Asa's info is also good stuff. I'd add that I always position the label on the tire at the tube stem. When I remove the tube I look for the offending hole. IF I've inadvertently just run over a huge, yet somehow unseen stinkin' rock or something...I look for a "snake bite" on the inside of the tube. (this would be a GREAT time to say you need to develop a "feel" for tire pressure. Thin walled, lightweight tubes leach out air and some need to be re-inflated before every ride. Feel what a fully inflated tire feels like on your bike after a full inflation and remember that your finger nail probably doesn't cause the tire to budge) So...if you forgot all of that and didn't check you tire pressure before you left home and you flatted, check for two little "snake bite type" holes on the INSIDE of the tube where they would come in contact with the rim should you hit some offending obstruction...like the edge of a curb, rock, stick...you get the picture.
No snake bite, use Asa's suggestion that you check the outside of the tire for little pieces of glass, wire, THORNS, etc. By using the label to always positon the tire/tube in the same relative location near the stem, when your find the hole you can now go back to the tire and say: Self...this hole is about 8 inches from the stem...look at tire (especially if you haven't danced around too much and know how the tube came out!) and search the offending area of tire for a sharp protrusion. Actually FINDING the offender will sometimes require re-inflating the tube to see where the leak is. (Sometimes the hole is SO small that I can't hear or see the leak. That's when I hold the tube up near my face and rotate it by my face. Often you will feel the rush of air as it passes by your face) Why do all of this? To Asa's point, IF you flatted because of say...a glass shard protruding thru your tire and you re-install your new tube into the old penetrated tire...VIOLA, you get more tool-less tire changing practice! Only THIS time you also get to pratice your patchings skills, too. You HAVE a patch kit with you...RIGHT?
Nothing you can find on the outside? Now you have to be REAL CAREFUL. First LOOK inside the tire in the area you've deemed the "offending area" with your tire label location trick. Can't see anything? CAREFULLY run your fingers LIGHTLY around inside the area. Many things like glass or wire will be picked up by your tire and then with each successive revolution driven further and further into your tire and then your tube until...PUFF...you flat! It may not be visible from the outside, but careful scrutiny on the inside will most often net the problem. (That's why it's important to QUICKLY wipe your tires with your gloves after you unexpectedly ride thru broken glass...you don't wear cycling gloves? 'Nother story!) I grasp the tire between to hands and kind of roll it inside-out so I can get a really good look. I've had multiple flats on the same tire because I simply couldn't find a stinkin' little piece of really sharp wire that was sticking thru my tire JUST far enough to flat over time. In defense of self...it was slightly bent, so I like to think it was screwing itself around making it even MORE difficult to find as I ran my hand around inside the tire after each flat thinking: it's GOTTA be in here somewhere...OUCH! Found it.
The label locator thing will go a long way toward allowing you to pinpoint problems, rather than whipping the tube out like some Rodeo rider after he just tied all four legs together on a roped calf...TA-DA!.