Mothing is fun and easy. I use a CFL black light projected onto a white sheet, but any outdoor light will attract moths if it is left on at night. Some serious moth enthusiasts build traps or put out sugary bait, but mothing need not get that complicated.
Identifying moths is a bit harder than attracting them. There are tens of thousands of species of moths, and while many are distinctive, many others are nearly impossible to identify by sight. In my experience most macromoths can be identified with some effort. One good online resource that I use is the Moth Photographers Group. Another good resource (for people on the west coast) is Pacific Northwest Moths. And of course, BugGuide is also helpful. There are some good print field guides, including the Peterson Field Guide to Moths of Northeastern North America (which I reviewed here) and other regional guides.
Data can be submitted to one of the websites listed here. Some websites like BugGuide and Project Noah will accept unidentified photographs, and volunteer reviewers will try to identify them.