Step 1 - Wort Cooling is not Optional
My first brewing setup was just about as basic as you can get. The two primary piece of equipment were a two gallon soup pot and a plastic bucket to ferment in. Obviously, there were other indispensible tools involved (hydrometer, thermometer, airlock, etc.) but the two workhorses were basic.
The great thing about brewing though, is that you really don't need a lot more. The things I've learned about the process of brewing are far more important than the tools I've added to my collection (which, if you ask my wife, are many). With what I know now, I'm confident I could go back to that original setup and continue to brew delicious beer. So don't be discouraged if you woke up Christmas morning with dreams of More Beer all-grain sculptures, and found a Mr. Beer instead. You can brew great beer with whatever you've got as long you take some care in doing it.
It can't be stressed enough that sanitation is the key to great tasting beer. If you perfect only one thing in your brewing process, good sanitation absolutely must be that thing. Nothing sucks like drinking a bottle of musty band-aids or throwing out five gallons of hard work. You're definitely not going to make any new friends brewing that kind of beer!
Since my first batch was ruined by poor sanitation, that was the first obvious improvement I needed to make in my process. Unfortunately, there wasn't just one weak link in my initial process. But I was new, so I had to take shots in the dark. So, what to fix?
The biggest problem I could think of had to do with worth cooling. I grossly over-estimated the cooling power of three gallons of cold tap-water.I poured it into my plastic bucket thinking it would bring 1.5 gallons of boiling hot wort down 70F EASY. I mean, it's 3 gallons! The wort is only 1.5! Right?!
So wrong. My first temperature reading was 120F. Now, I've heard of brewers pitching hot, but I don't think I've ever seen anyone recommend pitching at 120F. So, what to do? I eventually put it in the tub with six inches of cold water for two hours and got it down to 90F. Still far, far from optimal. We were due at a BBQ however, and it was either pitch then or leave it to sit for another three hours. Everything I'd read told me I needed to get that yeast working fast, so that's the side I erred on. Alas, the beer was ruined, for this and other reasons.
Next batch I wasn't going to leave the wort sitting around that long. I didn't want to spend any money at that point in time, so I did some digging and decided to try cooling the hot wort in a sink full of cold water. I've got a two sided sink with a big left side and a smaller right side. The pot goes in the left side, the faucet goes next to the pot, and cold water flows over the outside into the right side of the sink. Add some constant stirring to keep the wort circulating on the sides of the pot and you've got a cheap, effective cooling system. My original boil of 1.5 gallons would drop to 120 or so in ten minutes. My current boil of 2.5 gallons drops in around 20. Throw that on top of cool water in the fermenter and you'll generally get close to 70F.
Obviously, this isn't the optimal solution for everyone. If you're doing full boils, you're unlikely to have room in your sink to cool your he-man pot. You're going to need a chiller. Additionally, your wort is in contact with the kitchen air the entire time it's cooling. Granted, it's a reasonably short amount of time. Accidents happen though, and random elements (bugs, sneezes from five-year-olds, etc.) can definitely find their way into your pot. In that case, though, not even an immersion chiller is going to save you. Only a counter-flow chiller will keep you out of that kind of trouble.
But that's all fairly academic. I cool using my pot-in-water method and have had clean batches ever since I solved my other sanitation problems. If you're starting with a small pot and limited funds, it will serve you well. Just remember to actually do it, unlike my first batch!