On the road:
Find the puncture, unseat a few inches of bead, pull out that part of tube, apply self-stick patch.
Only if the damage is too large to use a patch, do I remove wheel and change tube.

Once I'm home:
If I used a self-stick patch, change tube, then use Rema fluid and permanent patch on punctured tube.
If I changed the tube on the road, then I apply permanent patch to the punctured tube.

NOTE: In my experience, the self-stick patches don't work in freezing temperatures.