A couple of people asked for a simple recipe for beer with household items.
I wrote a post on how I got started not that long ago, but I will reprise and expand on it here. Also for a more thorough and well thought out introduction to brewing Check out John Palmers How to brew.
Here's the deal, you need some equipment. Period.
At the very (very very least) you want a pot big enough to boil whatever size batch you are going to be making, keep in mind that when you add hops (unless you buy pre-hopped extract) this boil with get a crazy kick of head coming at you. You will need a vessel that you can attach an airlock to for fermenting into, and you will need something to put the final beer into when you are done.
Most homebrew stores sell for 5 gallon batches, most recipes you read are divisible by 5 gallons. 5 gallons gives you +/- 50 beers or just more than 2x24 packs. Normal people use bottles that are cappable, so you will need caps and a capper. When you do an extract brew you normally get 6lbs(or so) of LME(liquid Malt Extract) 1-2lbs of specialty grains (this give you mouth feel and color) and 2-4oz of hops for boiling and some yeast (normally one package of whatever they recommend). When you go to bottle you need to add (approximately) 3/4 of extra sugar (normally corn sugar because it is flavorless) to your beer before you bottle it to give the yeast something to eat so your beer will be carbonated. Are you getting all of this?
Sadly you need equipment for 5 gallons it is bigger than almost any normal person's biggest pot (I used a 7.5 gallon pot for my extract brews) My LHBS sells them for $40ish for acceptable pots. Some hombrew stores sell intro kits that comes with everything you need (except a pot) and mine included a free recipe of your choice. My kit was $100 came with one food grade bucket that is about 7 gallons and has a spigot. The value of this spigot cannot be overstated, I use this bucket every time I brew and bottle it is that useful. It also came with a 5 gallon glass carboy (the glass portion of this is somewhat rare as the carboys can be pretty expensive on their own) and airlock. The kit also came with a racking cane (that I wish was an auto-siphon but beggars cannot be choosers) a clamping hose for racking, a bottle wand and shorter hose for bottling and lastly an Red Barron capper. I think it came with a Hydrometer (for measuring your ABV% but it did not come with a beaker (tall skinny lab tool for samples).
Every piece of equipment listed has a use, and is part of the brewing process.
So come brew day you follow the same basic idea you start with 3-5 gallons of water and add your specialty grains normally in a muslin bag and cook them at whatever the temperature your recipie calls for (normally the a 154°F aka Saccharification temperatures for about 10-30 minutes). At this stage I call it making tea, you are getting the grains to the temperature that they give you the best and easiest sugar they have. After you're done making tea you kick up your temperatures rinse the grains and add your extract and bring you kettle to a boil. Once you see what is known as the hot break (when the little foamy head on your boil parts) and you start seeing a "rolling boil" you start your timer for 60 minutes and follow the recipe for hop additions. Normally you have a 60 minute and a 10 minute addition for simple recipes. When you add your hops watch out, this is when you are most likely to have boil overs, the hops piss off your boil and I don't know why.
At the end of the boil you wait for the temperature to drop to around 180°F naturally (you don't have to but it's kind of like letting meat rest before you cut it). I do this by putting the kettle on the floor of my garage and the cement acts as an immense heat sink but you have to move it round a bit. From here on out everything you do is basically trying to not fuck up the work you just did, if your beer is going to get infected it will happen during this stage. Now depending on how much water you have left in your kettle you add cold (like in your fridge overnight cold) water or ice to get your wort (the stuff you just boiled is now known as wort) down to yeast pitching temperatures. If your city has chlorine in the water you probably want to use bottled or filtered water (you probably want to any way) but getting your wort chilled quickly is the name of the game. You are trying to get from 180°F to ~80°F in about 15 minutes, this is known as the cold break. The point of this is to keep your beer from getting chill haze (cloudy when it is cold). There are some smart people that will tell you about the protein in your beer and how slow cooling affects the way that it coils, but you just need to know your beer will look cloudy if you don't chill it fast enough. Once it's cold enough you dump it into your primary fermenter (for me the food grade bucket) trying to splash it in there to get a lot of oxygen in it for the yeast to proigate. If you boil pot isn't big enough to boil the whole 5+ gallons you will do this first and then add cold water and ice to get to your 5 gallons total batch.
Now you pitch your yeast. Some yeast calls for you to re-hydrate them in warm water other people do fancy things with stir plates and yeast nutrient, for you if you ask the brewstore they have some yeast that comes in a smack pack (yeast in a pouch that has nutrients surrounding it) that will get you up and running very fast or there are yeasts that you can just pitch without re-hydrating. Whatever yeast you pick make sure you follow the package directions not what is written in your recipe, the people that packed your yeast know more about yeast than the people writing recipes on the internet. From there you attach your airlock and try to maintain the temperatures that are recommended on your yeast pack for several days until vigorous fermentation has completed (trust me you will know the difference). At that point some people choose to rack off (transfer from one vessel to another) so your beer isn't sitting on the trub (deflocculated yeast, proteins, and if you used hop pellets hops too). The trub is believed to cause off flavors in your beer, but you can and some brewers do leave it in one vessel for the duration of the fermentation. Temperature is important for your beer as too hot and you stress the yeast out (really really to hot and you could kill it) and too cold you cause it to go dormant. Some yeast does better in hotter environments and some does better in cold environments (lager yeasts) so if you cannot regulate your temperatures you should consider brewing for the season and use yeast to match the temps you can achieve. There is a whole lot to be said for yeast and keeping it happy, I'm reading a book that is dedicated to how to use and cultivate yeast Yeast: The Practical Guide to Beer Fermentation[?]. This is probably overkill for most everybody but the most interested in brewing.
Other things I use but there are alternatives for Star San and PBW (powdered brewery wash). Both are chemicals, my LHBS(local home brew store) sells the PBW in a measured for 5 gallon size that is great for cleaning bottles. You can use your primary fermenter if you are supper cheap, but I worry about all the gunk that comes from the bottle affecting my flavors so I use a cheapo home depot bucket for my cleaning. PBW cannot be understated as the coolest stuff, use gloves as it hurts my hands to use, but that could also be the hot as fuck water I use. You put the bottles in and the labels basically fall off no scrubbing needed (except for Deschutes stupid bottles the glue they use is awful). This stuff kills like everything including leftover yeasties from the beer you drank out of those bottles. You will need to rinse these bottles after you get the gunk off of them caution and time are well spent here getting clean bottles to put that beer you have worked so hard on. As a side note I've heard anecdotal evidence that the twist off style caps are prone to breaking if you plan on re-using bottles stick to the type you have to use a bottle opener on. After you are done I mix up a batch of Star San (this also is measured as a 5 gallon batch, but a little goes a very long way so I make it and put it into clean 1 gallon plastic jugs. You can try to eyeball the mix down to a more reasonable size batch but because I brew often the 5 gallons is handy to have around. I didn't mention it above but Star San is a part of basically every stage of my brewing process. It is a no-rinse sanitizer and I rinse every vessel and every instrument that touches my beer with it prior to use. It does not kill your yeast, won't add flavor to your beer, and is safe for consumption so don't be afraid of it, and use it everywhere. I have thus far not gotten an infected batch (even when my hands where in the chilled wort) and I attribute this to a liberal use of Star San.
After you have cleaned and sanitized your beer bottles (pro-tip if you clean them in your kitchen sink use your dishwasher as a drying rack for your beer bottles. Don't run them in the dishwasher if you have jet dry as it will leave a film on your bottles, but I use the washer as a drying rack.) Now that you have clean bottles you can transfer it into the bottles, cap and wait for them to carbonate. If you want to know your ABV% you take a hydrometer reader before you pitch your yeast, and before you put it in your bottles. The difference between your original gravity and your final gravity gives you the % of alcohol in the beer.
Hope this was helpful and not overly redundant, but if you want to work with household items I will try to think up the barest of minimum things you need. The trouble is you are going to be doing half or less batches and you have to scale them manually and this is a huge pain in the ass. Also if you don't have equipment to measure you don't know if it is pansy or good beer, and you won't know what to tweak for the next batch. In short I think bucking up and getting the starter kit I outlined in the previous post and doing 5 gallon batches. I know someone that has a lot less equipment then I do and he brews more often, and drinks more so it can be done with less equipment than I use, but the equipment I use has purpose and I use it to make the best beer I can. That said the beer that I am the most proud of and I though tasted the best was an extract beer so it can be done (it was a $75 5 gallon batch of beer so you know it was expensive).