There are several ways to produce hydrogen without too much hassle. Perhaps the simplest and easiest to acquire is putting electrodes into saline solution. A battery and salt water. Doesn't get much simpler. Actually plain water will do or you'll get chlorine on the O2 electrode if using salt.
Iron and low concentration sulfuric acid will do the trick as well. You can use calcium hydride and water, but that's not as easy to get nor as safe as either of the 2 above, I'd say.
Collecting the pure gas and putting it in a baloon in a field expedient manner may prove troublesome, however. <img src="/images/graemlins/smile.gif" alt="" />
I remember one very stressful final when I saw my chem prof running a battery through water. The electrodes were directly under an bottled filled with water and wraped with electrical tape. The gases displaced the water in the bottle forming a very pure ratio of 2 parts H and 1 part O. Funny, but when you hold said mixture in front of a bunson burner it causes the most unforgetable bang when the gasses reform into water. It's like a canon going off in a confined space. I'm just happy I had the test finished and saw it coming. Everyone else about soiled themselves on the spot.
That reminds me, I think there's a water filtration device that basically creates it's own chlorine in the manner described. Using a primer of some highly saline solution - capfull of water and a salt pill - and a quick zap of electricity, you get a whole lot of chlorine - useful for purifying water.
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Experience is a hard teacher because she gives the test first, the lesson afterwards.