Here are several tips for capturing images of old printed photos with your digital camera. With practice, you can even get results that come close to the quality of a consumer flatbed scanner.
I recently got back from a trip to Toronto, Ontario where I was visiting friends and relatives. On the trip I met an older friend of the family who is in her mid 90's. She knew my grandmother when they were both young kids growing up in Formosa (Taiwan) in the 1920's. During the visit I had a chance to see some amazing photos in her photo album from the 1920's-1950's. I took digital images of the pictures in the photo album with my Canon Powershot camera and they turned out really well.
One of the benefits of using a digital camera to capture images from an old photo album vs using a typical flatbed scanner is the photographic technique is gentler on the old book bindings and curled photos.

This is a photo from 1925 of a wedding in Japan.
Tips for Taking Better Photos
Hold the camera with both hands when you take digital photos of the pictures in your photo album.
Keep your hands as still as possible while pressing down the shutter button, and for a moment or two after the button has been pressed. This will reduce the camera shake that creates motion blur in the final image. If you still have a lot of camera shake, try holding your arms so your elbows touch your sides. This will give the camera extra support.
Set your digital camera to 400 ISO, or 800 ISO for a faster shutter speed. If the room is slightly dark you may have to set the camera to 1600 ISO so the shutter speed is fast enough to avoid motion blur.
Set the camera's focus mode to the flower icon (macro mode) so the camera will focus on close subjects.
When you want to get closer to the printed picture stay at the widest (furthest out) zoom setting, and manually move the camera body closer to the picture. This will give you the sharpest image. Digital cameras usually take better close up photos when the lens is at its widest zoom setting.
Try to capture your photos in a room with lots of natural ambient light. This will reduce the noise in the digital images. If possible, avoid taking pictures in dark rooms as the lack of light will cause the photos to turn out poorly.
If the printed photo is glossy or behind a sheet of plastic in your photo album try and position the photo album or camera at a slight angle to reduce the effect of the reflections on the surface of the photo. Tilting the camera a bit to the left/right or up/down can sometimes make a big difference in reducing glare on the photos.
After you take the first photo, it helps to switch to the image review mode on your digital camera. You should zoom in on the captured image with the zoom lever and make sure the digital photo turned out fine. Look for any blurring in the digital photo that wasn't present in the original image. If the edges of objects and people are blurry, you should increase the digital camera's ISO setting from 400 ISO to 800 ISO, then to 1600 ISO until everything in the image looks clear.
When you are zoomed in on the picture in review mode you can pan up/down/left/right using the standard menu navigation buttons on the camera.
Good luck and happy snapping.
Cheers,
Andrew