This page covers some basic brewing techniques, knowledge of which is assumed for all of the other recipes on this site. There are numerous other web sites and books about modern brewing that cover all of these topics in more detail than what I'm giving here, but I hope these notes are enough to get you started and give you some feel for my approach to brewing.
Mediaeval brewers didn't use sterilisation and it is possible to brew without sterilisation, but modern brewers will recommend sterilising anything that comes into contact with the brew. Sterilisation reduces the risk that your brew will be spoiled by unwanted organisms living in it.
There are several methods of sterilisation; I use a combination of boiling and chemical sterilisers.
Many brewing recipes call for some degree of boiling, and this will sterilise the liquid being boiled as well as the container it is in. You can also sterilise any utensils you have by submersing them in the boiling liquid.
A variety of chemical sterilisers are available from home brewing stores and are more convenient for sterilising fermenters, bottles and anything else that doesn't come into contact with the boiling liquid. They all work slightly differently, so follow the instructions on the bottle.
Your brew can be fermented using either open or closed fermentation.
Open fermentation. Mediaeval brewers, along with a few brave modern brewers, used open fermentation. In an open fermentation, the brew is simply left in an open container (called a "tun" or "fermenter") to ferment -- though you will probably want to cover the opening with a cloth in order to prevent insects and the like from crawling in. Many mediaeval recipes use a barrel with a hole in the top that allows the gases and dead yeast to escape.
While the yeast is working, the brew will bubble due to the creation of carbon dioxide by the yeast. When the brew stops bubbling, the yeast has stopped working and the brew must be bottled immediately. If the brew is not bottled quickly, organisms other than yeast will take over and spoil your brew.
Closed fermentation. Modern brewers strongly recommend closed fermentation as it is much less likely to result in a spoiled brew. "Closed" means that the brew is fermented in a container that has been sealed with an airlock. An airlock is a water trap that allows gases to escape from the fermenting brew, but does not allow anything to come in from outside the fermenter.
Home brew shops sell airlocks that are made from a plastic tube shaped something like a capital N. Half-fill the tube with sterilised water, enough that any air passing from the fermenter to outside must pass through the water. You can also make your own airlock by taking a tube from the opening of the fermenter and sinking the other end in a pool of water. Make sure the water end does not leave the water. Either way, ensure that the only way for air to go in or out of the fermenter is to go via the airlock.
As the brew ferments, carbon dioxide produced by the yeast will bubble out of the airlock. When fermentation stops, the airlock will stop bubbling and you can bottle your brew. As long as the fermenter remains sealed, the brew should be safe from spoiling. Once you have unsealed the container, however, bottle the brew immediately.
Never ferment in a completely sealed container. It will explode.
Duration of fermentation. The time taken for completing fermentatioin will vary according to the type of yeast you are using and the ambient temperature. Yeast packets will often specify the temperature at which they work along with the time they should take to ferment. At warmer temperatures (above 22C), fermentation will usually take around 4-5 days. At lower temperatures, fermentation can take longer and I have had brews that have taken up to a month to completely ferment in winter. Modern brewers often use heating blankets to keep their brews at the preferred temperature; these can be bought from home brew shops.
Do not bottle your brew until fermentation has completed. If fermentation has not quite completed, your brew will be gassy. If fermentation is a long way from completion, your brew may explode.
I mostly use 750mL glass beer bottles for bottling, and occassionally 375 mL stubbies. Many home brew shops sell cleaned 750 mL bottles but I find it more enjoyable to buy cartons of beer, drink them, and save the bottles for my own brew. You can also save the cartons for storing your own brew.
If you are making a fizzy beverage (e.g. beer), first add one teaspoon of sugar to every 750 mL bottle, or half a teaspoon to every 375 mL bottle. Use an equivalent proportion if your bottles are some other size. Fill each bottle to around 4-5cm from the top. After sealing the bottle, up-end it a couple of times to dissolve the sugar. It will take about two weeks for secondary fermentation to make the drink fizzy. Where I intend for a recipe on this site to be fizzy, I've explicitly added instructions to add sugar.
You can buy crown seals for sealing beer bottles from home brew shops. You can hammer them on using a cheap hand capper, or press them on using a more expensive levered capper. When using a hand capper, I use a phone book as an anvil against which to hammer; I found that bottles were liable to break if I hammered them directly against a hard floor. The large levered cappers are somewhat easier to use, less noisy, and less likely to result in broken bottles.
If you are re-using a screw-top bottle, you can usually just screw the cap back on -- be sure to turn it hard enough that the brew won't leak out when you up-end the bottle. If the screw cap has been lost or damaged, use a levered capper to put a crown seal on the bottle, and you should then be able to unscrew and re-screw the new cap.