I mostly agree with what Asanta said but to clarify one thing. Such illnesses may be caused by several different viruses and bacteria. Most bacterial GI illnesses are food borne where as viral causes of gastroenteritis can be transmitted by the oral fecal route ( hands get contaminated with your feces, you touch something, someone else touches it and puts something in their mouth). Because all of these illnesses are generally self limited and its difficult to tell a viral gastroenteritis from a bacterial one we usually refrain from using antibiotics which can sometimes make the diarrhea worse.
if this is Norovirus, and there is no way to know, you need to be sure to wash with soap and water since alcohol based products like Purell don’t kill this particular virus. In addition, surfaces should be cleaned with chlorinated cleaners. Keep in mind that Norovirus can remain viable on surfaces for 2-3 weeks after the surface becomes contaminated if it hasn’t been cleaned so you should try to clean any surface you may have touched from 1 day prior to your symptoms until 5 days after the illness