The most important factor in increasing your attenuation is yeast. You want to make sure you pitch an adequate amount of healthy yeast for the beer you are making as well as selecting a highly attenuating yeast strain. This generally means using liquid yeast as most dry yeast strains available aren't generally highly attenuative (with a possible exception of Nottingham English Ale Dry Yeast). The attenuation range of the liquid yeast strains is available on our website in the description of the yeast and also available from the yeast manufacturer.

In addition to pitching enough of the right yeast you can also add simple sugar; cane sugar, corn sugar, candi sugar and the like. Unlike malted barley/wheat simple sugar will ferment completely, decreasing your final gravity, increasing your alcohol content and lightening the body of the beer. Adding a small amount of sugar to an extract beer is often a good thing, but you don't want to overdo it or you will get a thin, watery beer.

If you are brewing beer from extract, boiling the full volume of your beer will help your attenuation. Many extract brewers do partial volume boils and top up their fermenter with water. This is a great way to save time, but the increased concentration of sugar can lead to carmelization, which makes your beer less fermentable (among other things). If you can't do a full volume boil, late extract additions can be helpful.

If you are all-grain brewing, increasing your attenuation is as simple as lowering your mash temperature.