First of all its a good idea to know if you are about to cry.
You are prone to crying if you:
Know when you are about to cry: If you feel your throat and stomach tighten and your nose itch, your head and chest ache, and your ears hum, then its likely that you are about to cry.
Once tears have fallen:
Look up: Just like the actors do. Like a saint. That will help your eyes absorb tears if they have just started or if there are only a few. This is also a good way of distracting people who may have seen you start crying. They too will look up to see what it is you are looking at. Take that opportunity to ...
Excuse yourself: If you are on transportation, this could be difficult. Otherwise, there are generally bathrooms available. Or deserted aisles to stand in, if you are shopping. Or if you are outside, find a tree to stand behind. Even if there are still people nearby, reducing visibility while tears fall is essential to crying gracefully in public.
Sit down but keep your head up: Crying takes energy so you will want to conserve it by sitting if possible. Watch out where you sit, though because dirt on your pants or gum on your jacket will last longer than the tears will. Keeping your head up will reduce redness in the face.
Keep tissues handy: Don't wipe, instead dab the tears from the side of your eyes or bottom of your eyes. Blow your nose slowly to reduce redness.
Take deep breaths: This will help get oxygen to your brain which contributes to a pleasant state of mind.
Stop focusing on obligations: Crying gives you the right to have a few minutes to do nothing and to think about nothing. So stop work. Stop reading. Stop talking. Stop walking. Stop writing. Stop typing. Stop watching. Stop everything for a few minutes and cry.
Treat yourself: Whether it's a nasty word or a smashed glass or the ordering of a rootbeer float. Do the first thing that pops into your head after you have stopped (see the previous paragraph).
Smile when ready: It is a good idea to place a smile on your face at the end of a cry. You deserve to feel good for completing the cry successfully. And placing the smile on your face will let others know that you have treated yourself and that the cry is over.