Some say brewing beer is like cooking, if you can follow directions you can brew beer. One big difference is you usually eat what you cooked fairly soon. A 5 gallon batch of beer might be around for a while. So its very important that after the beer cools below 170F you are very sanitary. Here are a few of my brew day tips.
Tip 0 - Clean it. Something can not be sanitized unless its clean. Use a good cleaner. I also recommend switching cleaners every few batches. I feel this makes sure any bugs don't develop a resistance and if one cleaner lacks in an area then the other might make up for it. However one good cleaning product might work also.
Tip 1 - Use a good sanitizer! I use Star San from Five star chemicals. It sanitizes very quickly, about 30 seconds. The foam will sanitize also. You can re-use it until its soiled or the PH drops below 3.2. You can spray it on gas connections and if they bubble then you have a leak. I usually have a tub of sanitizer sitting next to me so I can dip things in.
Tip 2 - Cover it! After you sanitize something like a carboy, wort chiller or bottles you should cover them. I use aluminum foil or plastic wrap. Minimize pet traffic and air flow if you can also.
Tip 3 - Chill fast. Once you are below 170F you are at risk of contamination. Chill quickly with a wort chiller or an ice bath. If using an ice bath make sure you have plenty of ice. Cooling works best if there is a good temperature differential.
Tip 4 - A healthy fermentation can make up for some sanitation issues. Its a competition between your yeast and other stuff so favor the yeast.