After accepting that life's going to suck for the next 12 hours, there are a few supplies that are going to make things more comfortable. They're also good travel items that come in useful even when your body isn't trying to turn itself inside out, so I'd recommend keeping these in your day pack anyway.
Recommended Supplies: Toilet roll, plastic bags, Imodium, hand sanitizer, wet wipes, large bottle of water, music, shorts, hair bands (for those with long locks) and chewing gum.
Most of these items are the result of straight up common sense for either keeping things in, aiding in getting them out, replacing what was lost or cleaning up after each bathroom dash. However, others may need some explanation. The music, for example, is there because 12 hours of stomach pain is fun for no one, so find something soothing on your iPod to distract you for the times in between toilet visits. Shorts and hair bands make it easier to keep everything out of the danger zone as your body empties itself in a variety of nauseating ways, whilst chewing gum temporarily rids your mouth of that all too familiar taste.
Depending on your mode of transport, it's worth considering an upgrade to something more spacious/comfortable if possible. You're also going to be wanting the isle seat and I doubt the passenger in the space next to you is going to argue.
If it's a bus without a toilet, bail immediately. You're not going to be making friends whilst you ask the bus to stop every half an hour when the expatriating comes at you unannounced.
Any pressure on your lower back is going to be uncomfortable, so if you have to chance to lie down on your side, take it. Otherwise, tuck something soft (like a pillow or scarf) into the small of your back.
This usually comes on strong at the beginning, getting less frequent as you go. For the moments where a mad dash is required, have a plan b in mind. Your stomach doesn't care if the bathroom is occupied so, in my case, I'd wait between train carriages looking much like the kid from The Exorcist.
By about 2am, the gauntlet between myself and an acceptable vomit receptacle had turned into a multi-discipline Olympic event. It incorporated the high jump (down from my bunk), the hurdles (over those sleeping on the floor) and the long jump (into the only available toilet). This would have been fun if failing said gauntlet hadn't meant covering up to eight strangers in unmentionable body fluids.
In parts of the world like India you're incredibly lucky if you find yourself in a plane/bus/train bathroom that is anything milder than horrifically dirty, so it's time to forget what you know about cleanliness and take care of business. You and this bathroom are going to be well acquainted by the time you depart, so find somewhere to hang your supplies and work on your aim.
You're ability to care about those around you is going to seriously compromised, but try to remember they're stuck in this also. Chew gum, clean yourself as best you can and find a quick path to the toilet that doesn't involve kicking people on the way past.
Also, avoid discussing what you passed and how you passed it because that's the kind of information only doctors want to hear.
Once you get where you're going, sleep, eat and drink well because you are going to be exhausted. One day should do the trick, but prepare to feel lethargic for a few more after that. If the vomiting persists, it's time to get medical advice. Remember, your body put you through a complete evacuation of anything that gives you energy, so take it easy and you'll be back to explorations and libations soon enough.