Sometimes the most indispensible things are the simple things. Case in point: tire repair kits. Nothing can ruin a ride like a flat tire and no repair kit, so be prepared.
Novara, REI's house brand for all things cycling, has an inexpensive and effective tire patch kit that contains rubber cement, sandpaper, five circular patches about 1.25" diameter, and two rectangular patches about 1.5" long. We used it to patch a tire on a Chariot carrier and it worked like a champ, even with our sloppy patching technique.
What it doesn't include are instructions. Even the Bike Repair App, which we like a lot, only includes instructions on replacing the tube, but nothing on an actual patch job. It's not difficult: inflate the tube and locate the leak; use the sandpaper to rough up an area slightly larger than the patch; smear some cement on the roughed up patch, and let it dry a few minutes until it's tacky to the touch; apply the patch and you're done.