I also change to a spare, while out on the road and then patch the damaged tube when I get home.
Trying to patch "in the field" almost always fails for me, but doing it with the right tools has been very successful.

I use Park Tool Super Patches. They are pre-glued and will flex and stretch with the tube.

1. Use a small amount of soap and water to clean the area to be patched, (this is to help reduce the release compound used during manufacturing). Since I don't always know where the hole is, I just do this while I am looking for the leak in the kitchen sink. Allow the tube to dry thoroughly.

2. Scuff the tube around the puncher. Sand paper seems to work better than the dimpled tin piece that comes with some patch kits.

3. Apply the patch at a 45° angle to the rotation of the tire. This gives the adhesive more surface area in the direction that will get the most stretching.

4. Use a C-clamp with a piece of old inner tube around the one being repaired to keep pressure on the patch as the glue cures. Another option is to put a stack of books on the inner tube. I usually leave it this way at least overnight; 24 hours, if I have time.

Happy patching!