Here are seven tips that will help you on your quest.
Keep Your Shutter Speed Above 1/80
The biggest culprit of bad snapshots is motion-blur. If you are shooting in low light without a flash, most cameras in auto will choose a shutter speed that is way too low. Move to shutter priority mode ("S" on most cameras) and just keep it at 1/100. Many say 1/60 is good enough, but 1/100 is a safer bet amidst the chaos of a family gathering.
Shoot In Bursts
If you are taking candids, it can be hard to capture the one split-second where the baby cracks a smile. Use your camera's burst mode and fire off three or four shots so you don't miss the magic moment.
This is fairly obvious, but well-done candids are always more memorable than posed portraits. If you think about it, it's kind of creepy having dozens of shots of people grinning wide-eyed at the camera. Candids are harder, however, and you have to take a lot to have a good set of keepers. So don't be shy.
Everyone focuses on faces and smiles, usually at the neglect of the bigger picture. Step back and snap a couple of nice wide shots of the entire room full of people — far enough away to hide your drunk uncle's drool and your grandmother's creepy stares.
Break People's Bad Picture Habits
Some people have a gut reaction whenever they see a camera pointed at them to look at it, freeze and smile. If your subjects do this, don't take their picture! Either politely lower your camera until they resume doing less contrived things — or simply tell them to stop it.
Use Fast Prime Lenses
Most traditional holiday activities are indoors and in dim light. In these conditions, fast prime lenses (f/1.2-f/1.8) will let you take better images without resorting to that 1,000,000 ISO setting with more noise than photo. Also, you will be able to achieve those great shallow depth-of-field shots that make any family photo album look pro. If you can, have a good wide angle and a good medium-telephoto lens on hand.
Shoot Scenery And Decor
Again, you gotta move past boring ol' faces. A set of photos should tell a story, and that includes the locale, the decor, the food, the weather. ALL OF IT.