The best way to eliminate clutter from your photos, of course, is to recognize it before you snap the shutter and then avoid it or crop it away in the viewfinder. That's easier said than done because a lot of times when you're shooting casual pictures it's about capturing the moment and not perfecting the composition. One good example of this is when you're sitting around the dinner table at a holiday gathering or an informal party. I love to keep the camera with me at dinner and shoot informal or candid portraits--particularly when people are relaxing during the after-dinner tea and desert.
The problem with shooting portraits around the table, however, is that there are usually a lot of used dishes and half-empty glasses, crumpled napkins, etc. If you stop to clean up the table before you shoot, you'll lose most of your subjects and probably get tricked into clearing off the table. It's safer to just keep shooting and rely on your clever editing skills to clean up your shots later.
There are a couple of different ways to tidy up a messy shot in editing. You could, of course, crop away some things and perhaps clone away others, but I've found a quick-fix solution that takes only a minute or two and that is to simply paint away the areas you don't want to show. Granted, it's not the most refined method of cleaning up a photo, but it's fast and it works and if it's done well it can actually look quite artistic. To prepare for painting I first duplicate the background layer (Command J on a Mac, Alt J on a PC) and then do my painting in that layer. That way if I don't like the effect, I can simply trash that layer and create another--much faster than going back and erasing strokes you don't like.
Also, before I begin to paint I do my basic set of corrections by cropping, adjusting the color and exposure and then sharpening the image. Once that's done I simply grab a paintbrush from the brushes palette, choose a color and then quickly paint away the edges of the frame as I did here. In about a minute I was able to get rid of two stray hands (one on either side of the table), an extra wine glass, a butter dish and a few napkins--the typical remnants of a dinner party.
The trickiest part of the using this technique is choosing the right style of brush while also paying close attention to both brush hardness and size. I actually tried about five different brushes for this shot and finally settled on one that painted a broad swath (to make things faster) but that had an artistic paintbrush edge to it. As you paint, remember that you can "pull" the stroke from any direction--up/down, side-to-side, curving swoops, etc. Once you start painting in one direction though it's usually best to keep working in that same direction--but that's really something you can decide as you paint. I've just found that if you change the direction or angle of your strokes, things start to get a bit chaotic looking and end up looking more like a kid's finger painting (which is fine if that's the look you're after and might be fitting if it's a shot of a kid's birthday party).
You can also choose a color of paint to match your subject or, as I did here, just white it out and you can also adjust the opacity so that you can see through the paint if you like or make it 100-percent opaque as it is here. You can even paint it a few times while changing the opacity of the brushes--doing the far edges at 100-percent to completely cover the background, for example, and then fine-tuning the inner edges with, say, a 75-percent brush. Experiment and you'll find tricks that work for you.
As a final step, particularly if you're using white around the edges, I like to create a black frame around the image to separate it from the white background of the printing paper (or in this case the screen background). To do that simply use the rectangle tool to draw a box around the edges of the frame, then go to Edit>Stroke and use a two-pixel wide stroke using black as your color; that will turn the box you've drawn into a frame--it's very simple.
This may not be the most refined method of cleaning up a shot, but knowing that you can paint away a lot of clutter with just a few minutes work will make you more likely to shoot fun family photos regardless of how neat the setting or background happens to be.