Uposatha day is the day when the vinaya is recited. The vinaya is of course the list of all the rules that monastics follow.
In Asia, there are well defined community practices. For example, people go to the local temple that day, or in Mahayana Buddhism, you might fast (i.e. eat vegetarian) that day, or make a stronger effort to follow the five precepts or maybe follow all 8 precepts.
Out here in the west, not a lot of community practices visible to me. I personally try to make up for it by re-reading my favorite list of rules, the "Brahma Net Sutra" on Uposatha days, which is the same thing that real life east Asian Buddhist monks do.
I suppose a lay follower who wants to keep to the spirit of the holiday, but didn't want to read or recite a particular moral code, might do a sort of "Weekly Review" like you see in system of personal productivity, except with a Buddhist theme, e.g. http://lifehacker.com/5908816/the-weekly-review-how-one-hour-can-save-you-a-weeks-worth-of-hassle-and-headache