Static is a serious problem because it's easy to generate voltages that exceed the maximum 1,500V - 3,000V protection level of most chips, especially in winter when the furnace is running and keeping the humidity below 10%. All types of chips are susceptible to static damage, not just CPUs and GPUs; even old style bipolar chips can be damaged by static.
The easiest practical way to avoid static is by working on a big anti-static surface, barefoot and in short sleeves. Short sleeves cause your elbows to come in frequent contact with the anti-static surface. You can buy a 30' roll of 24" wide pink anti-static bubble wrap from Staples for under $20:
http://www.staples.com/Staples-Anti-Static-Extra-Wide-Bubble-Wrap-24-inch-x-30/product_657404
A wooden or Formica table top isn't too bad for static, while plastic table tops can be horrible. Metal surfaces don't create static but can't be used with motherboards because they can short out CMOS batteries.
Don't think you can protect against static by setting components on top of metalized plastic bags because the vast majority of them are designed to be anti-static only inside. So if you want to use them for protection, turn them inside-out. However don't apply power to anything sitting on such a bag because some of those bags can conduct enough to create bad shorts, especially the opaque bags that are stiff (aluminum foil covered with clear plastic).
Anti-static bracelets work very well but require proper use. For example, if you're installing memory into a computer, you want the bracelet grounded to the computer case, but what if you remove the memory from its anti-static packaging but don't immediately install it but instead set it down on a table that generates static?
Regular gloves can make static worse, but there are anti-static gloves.
Most synthetic carpeting isn't too bad but will still generate damaging voltages. Spraying the carpet with diluted fabric softener helps a lot.