Visiting a cemetery is a very hands-on way of doing research and collecting family history information. You can locate cemeteries with family members through various online cemetery records, obituaries, or from living family members.
Tombstones can provide you with quite a bit of information about the people buried there. Birth and death dates are the most obvious, and are found on most stones. Symbols on the stones may indicate religious affiliation, which can help you locate church records. Siblings, children or spouses are frequently documented on gravestones, possibly with birth/death dates of their own. If the deceased was in the military, you will likely find rank and unit information, which can be very helpful when searching through military records. Membership in other organizations (such as the Knights of Columbus, or the Order of Elks) may also be recorded on a gravestone.
More detailed name information can be found as well, such as middle names or maiden names (for the women in your family). A woman's maiden name is often marked with née, which is French for 'born'. Using my own name as an example, it might read Darlene Vaillancourt née Furlong, with Furlong as my maiden name.
Also, check nearby graves for other closely-related family members you might not know about.
Tombstone rubbings have long been the standard way of recording what you've found. A large piece of paper would be held against the grave marker, and rubbed with charcoal or chalk to create an image of the stone carvings. An easier method is just taking a photograph, especially when dealing with very old (and unstable) tombstones. Digital cameras are a great tool for cemetery visits. Don't forget to check the back of the stone.
Above all else, be respectful when visiting a cemetery. Walk around, not over, the graves and don't disturb any visitors who may be nearby. And speaking of visitors, if you find fresh flowers on a relative's grave, you might be able to find living relatives you didn't even know you had.
