#1 - Sanitation - make sure anything that touches your wort/beer is properly sanitized
#2 - Fermentation - pitch the right amount of yeast (stick to dry yeast until you're ready to start making yeast starters), and control your fermentation temperature (mid-60's F is a good temp range for most ales. Keep in mind that fermentation produces heat, and the actual beer temp will be a few degrees warmer than ambient temp)
#3 - Quality Ingredients - use the freshest ingredients you can find. The major online shops do enough volume where you can be pretty confident that their extract and grains are pretty fresh. Keep in mind that crushed grains and liquid extract lose their freshness fairly quick. Don't buy a kit and sit on it for a few months before brewing.
#4 - Take detailed notes - it's hard to know what you did right, did wrong, or want to change for next time unless you know exactly what you did this time. Brewdays rarely go perfectly, especially when you start. There's always room for improvement, even for the advanced brewer.
#5 - Don't overcarbonate - your kit probably came with 5oz of corn sugar for bottle priming. This is usually a bit much for most beers if you use the whole thing. Use an online calculator and measure out the correct amount for the carbonation level you want. Dissolve it in some boiling water and mix it into the beer in your bottling bucket with a sanitized spoon. If it is not mixed in evenly you will have some flat bottles and some overcarbonated bottles. Here is a good calculator I use: http://www.brewersfriend.com/beer-priming-calculator/
#6 - Whatever you do wrong, always remember that malt + yeast = beer. The vast majority of the time you will end up with a tasty brew even if something goes wrong. Ride it out, enjoy your results, and keep in mind that you can probably do it even better the next time.
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