With so many digitized copies of original source documents now available online, I've found one of the quickest ways to get my reticent relatives interested in discussing their family history is to take them online and start showing them what can be found. A 1930 census record of my paternal grandmother's family that I showed her online last year prompted at least an hour of stories about her siblings, the house they lived in, the neighbors, her Dad's job, and more!
Census records are obviously a good place to start with relatives, as they often end up fascinated besides themselves to see their name, or the names of their parents or grandparents listed along with details on occupation, children, etc. FamilySearch Record Search is a great place to check first as they have a large collection of free census images for viewing. Passenger lists are also popular for families with recent immigrant ancestors. Subscription Web site Ancestry.com offers an extensive collection of U.S. and U.K. passenger lists, as well as census records for the U.S., Canada and the U.K. A free trial offers you a chance to check out their offerings if you don't already have a subscription.
Newspaper articles, including marriage notices, obituaries, and a wealth of human interest stories, from school contests to trial proceedings, can also be a good way to spark the interest of people who "aren't into genealogy." You may want to do some initial searching for articles before you sit down in front of the computer with your relative, because full-text searching of newspapers can be a bit tedious at times and cause them to lose interest quickly... Many relatives find death certificates interesting as well...and they often include burial information so you can plan a road trip to the cemetery.
The Irish surname Neville was also anglicized from the Gaelic Niadh (hero).