This is a summary of some of the better tips I've collected over the years for making better beer. - BrewWiki
1. Keep it Sterile
Anything that touches your beer after it has started cooling must be sterilized using any of the popular sterilizing solutions (bleach, iodophor, etc). The period immediately after you cool your beer is particularly critical as bacteria and other infections are most likely to take hold before the yeast has started fermentation.
2. Use High Quality, Fresh Ingredients
The quality and freshness of ingredients is very important. If you started with dry yeast, move up to liquid yeast and your quality will improve. If you are an extract brewer, try to get fresh extract rather than a can that is several years old. Store liquid yeast in the refrigerator and hops in the freezer. Hops, dry malt, yeast, liquid malt and crushed grains all have a limited shelf life and must be used quickly. Crushed grains, dry malt and liquid malt will oxidize over time. Hops bittering power declines both with oxygen (purchase it in sealed foil bags if possible) and temperature. Whole, uncrushed grains have a long shelf life, but must be kept in a cool place with low humidity.
3. Cool the Wort Quickly
Cooling your beer quickly will increase the fallout of proteins and tannins that are bad for your beer and will also reduce the chance of infection. A wort chiller is a relatively inexpensive early investment that will improve the clarity and quality of your beer. Cooling is particularly important for full batch boils.
4. Boil for 60-90 Minutes
Boiling your wort performs several important functions. It sterilizes your wort, vaporizes many undesirable compounds, releases bittering resins from the hops and coagulates proteins and tannins from the grains so they can fall out during cooling. To achieve all of these noble goals you need to boil for at least 60 minutes, and for lighter styles of beers a longer boil of 90 minutes is desirable.
5. Control Fermentation Temperature
Though relatively few brewers have dedicated fermentation refrigerators, there are simple methods you can use to maintain a constant temperature for ales during fermentation. The best technique I've seen is to pick a cool, dry area in your home and then wrap the fermentor in wet towels and place a fan in front of it. Wet the towels every 12 hours or so, and you should get a steady fermentation temperature in the 66-68F range. Most brewing shops sell stick-on thermometers that can be attached to your fermentation vessel to monitor the temperature.
6. Switch to a Full Batch Boil
As mentioned above, Boiling your wort provides a large number of benefits to your beer. However if you are only boiling 2-3 gallons of a 5 gallon batch, then you are not getting the full benefits of a 60-90 minute boil. The purchase of a 7-12 gallon brew pot and (highly recommended) outdoor propane burner (which will make the spouse happy as you now brew outside) are great intermediate steps for moving to All Grain brewing and the full boils will improve your beer.
7. Don't Use Plastic Fermentors
Glass carboys (or stainless) fermentors offer significant advantages over the typical plastic bucket. First they are much easier to clean and sterilize ?. Second, glass (or stainless) provides a 100% oxygen barrier, where plastic buckets are porous and can leak oxygen if stored for long periods. Third, plastic fermentors often have very poor seals around the top of the bucket and can leak in both directions making it difficult to determine when fermentation has actually completed. A 5 gallon glass carboy will do the job better, and is available at a very reasonable price from most stores.
8. Make a Yeast Starter
While pitching directly from a tube or packet of liquid yeast is OK, your beer will ferment better if you make a yeast starter first. Boil up a small amount of dried malt extract in a quart of water. Cool it well and then pitch your yeast into it 2-3 days before you brew. Install some foil or an airlock over it and place it in a cool dark location. When brew day comes, pitching your starter will result in a quicker start and less risk of infection or off flavors.
9. Make Long Term Purchases
You may have started brewing with something really simple, but if you enjoy brewing and think you might stay with it, then you are best off making long term purchases rather than a series of short term purchases. For example, early on I bought a 3 gallon pot, then a 5 gallon pot, then an 8 gallon enamel pot and finally a 9 gallon stainless. It would have been much cheaper to jump to the 9 gallon stainless after the 3 gallon pot. Similarly I've had several sizes of immersion chillers, finally settling on a two stage 3/8" diameter copper coil. If you instead make long term purchases (a good pot, a good chiller, glass carboys, a nice mash tun/cooler) you will save a lot of money in the long run.