I've had a bit of practice, but it's really not that hard. This is no craft brew, and certainly not a time honored family recipe. It is tasty on a hot day.
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Buy a pre-hopped extract. I made a Cooper's Bitters recently. This one says to add 1 pound of sugar, but I use prefer to use one pound of Dried Malt Extract (DME).
- Acquire a food safe plastic bucket + lid. Buy one, or ask a local restaurant for a used one.
- Acquire some food safe plastic tubing. I couldn't find anybody to borrow, so I bought it.
- Buy some bottle caps and a capper.
- Acquire an air lock and rubber stopper.
- If your bucket doesn't have a hole in the lid, drill a hole in the bucket's lid so the stopper/airlock will fit snuggly.
- Wash the bucket, lid, stopper, airlock, and a big wooden spoon. Don't use soap. Make sure it's visibly clean, then soak in diluted bleach. Rinse with potable water.
- Put 4 gallons of potable water in the bucket.
- Dump pre-hopped extract and sugar/DME into the bucket. Stir until dissolved. Dump yeast packet (it came with the extract) in the bucket.
- Put the lid on. Insert rubber stopper into the hole, fill the airlock with water (to the line), and put the airlock in the stopper.
- Let sit for 3-14 days, until it stops bubbling.
- Clean ~50 used beer bottles (prefer the kind that need a bottle opener, but twist-off will work, they're just harder to cap). Soak tubing, bottles, and caps in diluted bleach. Rinse everything with potable water.
- Using the food grade tubing, start a siphon, and fill as many bottles as you can. Leave some room in the bottle; fill it to the same level as store bought bottles.
- Add a teaspoon of sugar/DME to each bottle for carbonation. Measure carefully, err on the side of less sugar. If you add too much sugar, you may be making a CO2/glass bomb. Cap bottles.
- Let bottles sit for 3-5 days at room temp.
- Chill bottle and enjoy.
The most important step is cleanliness. Make sure everything is visually clean, and not scratched. Make sure everything has been in good contact with the dilute bleach. Make sure the bleach is well rinsed before it touches the ingredients/beer. If the beer gets moldy, or doesn't look/smell like beer when you're done, don't drink it.
There a many different techniques and gadgets for every step in that process. Every step can be expanded and customized to make the beer more uniquely yours. You will get better results with better equipment and a better process. But you dont' have too. This process, plus a can of pre-hopped extract will reliably make decent beer. It's not good beer, but it's better and cheaper than american mass-brews. This process costs US$20-30 to setup, and about $20-25 for 2 cases of beer. If you're really cheap, you can make it cheaper (use a growler instead of bottles+caps; use sugar instead of DME).
If you're interested, I recommend Complete Joy of Home Brewing. If you're already a brewer, and you don't believe me that you can make beer with this setup, then I recommend The Alaskan Bootlegger's Bible.