BigFloyd said it correctly. I'll 2nd his comments.
For a beginning brewer, the following are the most common mistakes.
1. Unsanitary tools, buckets fermenters etc.
2. Not enough yeast. One vile/smack pack is fine for a simple ale, if the yeast is viable and hasn't begun to deteriorate. I think that by the time you buy the yeast it has already deteriorated some. I think that every time you make beer, See Mr. Malty's Yeast Calculator for the correct amount of yeast.
3. Yeast aeration and nutrients. Shaking the carboy gives you about 8 parts per million (PPM) of O2, while using an air pump along with an aeration stone and air filter will give you the right amount of about 12 PPM. O2 gas can give you 12 PPM and more if needed (i.e. High ABV Barleywines). A stainless steel aeration stone kit at your brew shop can hook up to a cheap O2 bottle from the hardware store, and works great.
4. Temperature control: This is extremely critical when making most beers. Most ales ferment around 65-68°. The best way to know what temp works best for the yeast, go to the manufacturers website. When your yeast is too cold it hibernates. When it is too hot, it gives off horrible off flavors similar to nail polish remover. The yeast flavors are part of the profile of the beer. So if you don't treat them correctly, your resulting beer will taste awful.
5. Finally, the other very critical part is Oxydation. When your beer has finished fermenting, it is absolutely critical that your beer never come in contact with Oxygen/air. If so, it will give off cardboard like flavors and make your beer dull and boring. This could be the "woody" flavor you were mentioning.
6. Water: This makes up a large portion of your beer. Taste your water, do you love it, hate it or what? Try using Reverse Osmosis water and throw in 3 grams (and up to 5 grams) of Gypsum per 5 gallons for a bright taste that gives a dryness and accentuates the hops. For beers that you want a soft, sweet and opposite of dry, try 3-5 grams of Calcium Chloride.
Cheers