I often encounter a situation where I have coffee, hot water, sugar, and Styrofoam cups, but no spoon. How do I effectively mix the ingredients?
When it is clear that it is only me drinking this coffee I use this trick: I take a first sip and, while still having the cup in drinking position, I "blow" the coffee back into the cup so that the created turbulences sirres up the sugar at the bottom.
I always wondered if this is considered inhygenious by someone, but it works for me.
Use your finger (if your coffee is not too hot and your finger is clean) as seen in 10 Years movie.
Maybe this is a variation on other answers, but one option is to make sure the cup is significantly bigger than the amount of coffee you are drinking to allow room to safely 'swirl' the coffee and ingredients together. If there's a lid, you can get away with a little less room. If it's one of the lids that has a closable sippy hole, you may even get away with actual shaking the coffee (though obviously ensure that the lid is held on tightly as you do)
If you don't want to pull anything in the cup, there still is a (very simple) way. Not very effective but it works.
Just stand upward, hold the cup in front of you and turn in your own axies. The liquid in the cup will turn counterwise while the cup will not.
The "mixing-force" is very weak in this, so sugar which has not dissolved completely ain't affected by this very well. But if you can wait a view minutes after inserting sugar, or if you only use milk, it works well.
This may not strictly answer your question, but two possible suggestions with one main point: Avoid the situation!
1) Always carry a stirrer of some sort with you. Try a small measuring spoon -- often the smaller measurements aren't too long and since they're often held on one ring or chain as part of a set, you can use attach it to your key ring (assuming you have a tissue or something to wipe it with)
2) Use a self-stirring mug (search google or ebay) rather than the provided Styrofoam ones, though I realize this may not be feasible if you're traveling and can't carry the mug.