Imagine you're standing at the end of the block shouting at your kids to stop roughhousing. The more empty space between you and your brood, the less you'll be heard. If you're in the house watching them rolling around on the lawn, you'll have a similar problem. The walls of your home will trap the sound of your voice, and less of what you say will make it through the wall to them. Distance, nearby sound dampening materials and solid barriers (mass) make good soundproofing.
You may not be able to move your home to the middle of nowhere, but you can put sound absorbing materials between you and sound, or between the sounds you create and the outside world. Sheetrock and brick are both great soundproofing materials, but the beauty of adding mass is that things like bookshelves (complete with books), drapes and carpeting all help dampen sound, too.
Another option is to add insulation and soundproofing to your walls. The empty spaces inside your walls help deaden sound, but insulation does an even better job. You can use special viscoelastic sound dampening material, but even standard insulating materials will provide some added soundproofing.
Sound seeps through cracks and crevices and exits (or enters) through the same spots where air can escape -- the same areas you're on the lookout for when insulating your home from heat loss. Loose window seals, gaps in baseboards, cracks and crevices are all areas where sound can penetrate. Weather stripping, sealer and silicone caulk insulation will help block sound transmitted at these sites. While you're at it, don't forget to insulate your wall plugs, and cap them, too.
Noise can redouble as it bounces from place to place. It's like the gift that keeps on giving -- in a bad way. Added mass helps absorb sound vibration, and the more textured the material (think nooks and crannies), the better it will trap sound and curtail its ability to jump around.
Having lots of overstuffed furniture, a sealed environment and insulated or thick walls will help soundproof your space, but you may still need additional soundproofing. One of the quickest ways to add soundproofing power to a room is with acoustic tiles: porous tiles designed to grab sound and keep it from reflecting back into the space. Typically, the more sound absorbing materials there are in your room, the fewer tiles you'll need. Acoustic tiles are available for both ceiling and wall installation, and tiles are usually rated for noise reduction efficiency. You'll be able to get a good idea of the impact they'll have in your space before you buy.