1. Read Reviews
Although it seems silly to state in this day and age, reading reviews is essential. It doesn't much matter if an appliance uses the least amount of energy and saves you the most money if it doesn't run well or starts to go downhill after 3 months of constant use. Reading up on multiple websites is an excellent place to start!
2. Learn To Read An Energy Star Label
Though it's not too tricky to walk into your local appliance retailer and locate the prettiest model, do you know how to find the one that's the least expensive to operate? Check out the graphic above for a break down. At the top you'll find the make and model (along with a list of major features), along with the manufacturer and size. Below that the big yellow label will tell you how much energy it will consume each year. This won't mean much until you look at the scale directly below it, which states the high and low usage for other appliances in the same size category. Last but not least, you'll find the yearly operating cost, the bottom dollar if you will.
3. Think Ahead
When purchasing a major appliance, think of it being with you for the next 10-20 years. Obviously, there might be bigger and better models that come along as the decades pass and there's a good chance you'll upgrade, but when thinking about the bottom dollar, figure your amount saved over a 10 year period. This is especially important if you plan on selling your home. Being able to say you have top of the line energy savers always sounds good to new buyers!
3. Don't Discount Small Electronics
Smaller personal electronics like telephones, televisions, printers and stereo systems won't come with an energy star label. This isn't because they are inefficient in the power department, but there isn't as large of range in power usage between the different models. There are some differences, for instance, ink jet printers use less energy than lasers and LCD televisions and monitors draw less power than CRT or plasma screens, and things with small lightweight power supplies tend to be more energy efficient than large, heavy transformer-based power supplies.
Additional Notes: Always make sure to read up on any ongoing incentives for purchasing energy efficient appliances, there's rebates, refunds and tax breaks everywhere you look these days. Hit up the Energy Star site for a list of rebates possible for all sorts of appliances and where they're given. You can also check out a few notes on what to look for in specific appliances to find ones that will be the most efficient and give you the best bang for your buck over at Natural Defense Resource Council (ex: Chest Freezer keeps in more cold than upright models).
(Images: Flickr members Josh and Melanie Rosenthal licensed for use by Creative Commons, Sarah Rae Trover, Consumer Energy Center, Amazon, Flickr members edkohler & disrupsean licensed for use by Creative Commons)