Many things contribute to "extract twang."
1) Using old ingredients. If the LME you're using has been sitting on an unrefrigerated store shelf for a long time, maillard reactions will begin to occur. This will lead to beers that are darker in color than expected, as well as off-flavors. If you buy liquid extract, make sure the place you buy it from has a rapid turnover rate. This will ensure that the extract you buy is fresh. If you're not sure how old it is, then use dry extract. It holds up over time much better. Refrigerate your liquid extract.
2) Adding extract to your pot while it sits on the burner. DO NOT add your extract while your brewpot is sitting on the burner. Remove the pot from the burner, then add your extract and stir it in until you know it is fully dissolved into the water. Liquid extract tends to sink to the bottom of the brewpot. If you add it to the pot while it is on the stove or burner, you run the risk of scorching your wort, or creating more of the aforementioned maillard reactions.
3) Adding all of the extract at the beginning of the boil. This is a common mistake made by newbies that isn't their fault. Many books and kit instructions tell you to add all of the extract at the beginning of the boil. BIG MISTAKE! A concentrated boil leads once again to those maillard reactions. Your beer will have that undesirable cooked extract flavor. Use the extract late method. Add a third, to half of the extract at the beginning of the boil, then the remaining in the final 15 minutes of the boil, or at flameout (I prefer flameout). This will greatly improve both the color and the flavor of your beer.
4) Use a sound recipe. I love when people formulate a recipe that starts with 2-3 lbs of steeped crystal malt, along with all amber or dark malt extract. Then when their beer tastes funky, they blame the extract. There's nothing wrong with using darker extracts, but you have to consider what is in them if you're going to use them. Amber and dark extracts already have crystal malt in them, so if you're going to add more crystal malt to them (and often when using these extracts, you do not need to), do so sparingly. No more than a pound, and even then know that your beer is going to be pretty malty. I know most people advocate using only light extract, and getting your color with steeping grains. It is a sound practice, and it gives you more control over your beer. However, if you know what a darker extract will add to your beer, then there is nothing wrong at all with using them.
5) Not chilling your wort quickly. After the boil, you should get your wort cooled, and your yeast pitched into it as soon as possible. A wort chiller will help you accomplish that. You can buy one, or build one yourself. Rapid wort chilling after the boil made a huge difference in the quality of my beers.
6) Poor fermentation control. This is one of the most crucial steps to brewing great beer. You must do your best to ferment your beers under 70 degrees (unless you're brewing Belgian). It's difficult to do in the summer. If you can use a spare fridge, then you've got it made. If you don't use a swamp cooler and a forgiving yeast strain, as another poster mentioned.
Sorry for the novel.
