Once your cooled wort and yeast are in the carboy, you need to put an air trap on the top to allow air to escape but keep air (and dust and yeast and bacteria) from getting in. A perfectly good air trap can be purchased for less than two dollars. It fits into the hole in the center of a rubber plug for the carboy. If you don’t have a trap, you can use a flexible hose inserted into the rubber plug on one end and then into a jar of water on the other. Depending on where you are leaving your beer to ferment, you might find the jar of water troublesome.
For the first 12 hours, while the fermentation is getting started, the carboy should be in a spot between 65 – 80 degrees Fahrenheit depending on the yeast. Most brewer’s yeast packages state on them the ideal temperature for getting the process started. You can buy a simple standing thermometer at a hardware store to place next to your carboy to monitor the temperature. If it is too cold, it might prolong the period before fermentation happens but it could also prevent fermentation. Your goal is to have the yeast start to rapidly multiply, eat the sugars and create alcohol, before other organism that happened to fall into your brew have a chance to multiply. The alcohol will kill any intruders but you need the alcohol to build up first. It is a microbial battle and you are aiding the yeast side.
I put my carboy up in the middle of my Wedgewood stove where the pilot lights keep the temperature around 70 degrees. I put a couple of dish towels under the carboy so that the bottom doesn’t get too hot. The carboy needs to be covered with a towel or something to keep light off the liquid. Light will ruin the flavor. I use an old sweater my daughter outgrew. It fits perfectly. After a few days, I move the carboy to the top of the refrigerator to have it out of the way.
You should see the brew start to bubble in 12 – 24 hours. There should also be a nice foam on the top of the brew. If it doesn’t start to bubble within 24 hours, there is probably something wrong. It could be that the yeast was bad, or the temperature was off, or your wort got very contaminated – enough to hinder yeast growth. You can try adding more yeast to see if that starts the fermentation. If this is unsuccessful, you might need to start again.
I have to say that this has never happened to me. If you are careful with sterilizing, are nice to your yeast (keep it in the refrigerator until a few hours before you are ready to use it) and buy good quality brewer’s yeast, you should have no problems.
I remember that when I started brewing beer, I was concerned that I would buy the equipment and the ingredients, spend time on the wort, and then the beer wouldn’t work out. It would be like working hard sewing a bathrobe only to have it look terrible. However, I have yet to have a beer fail. If you do everything as you should, the chance of failure is small indeed. The chance of making a delicious beer is quite high.
The beer might bubble away for a week or might just bubble like crazy for 36 hours and then be done. Even if you see no more visible fermentation taking place, you should still leave the beer in the carboy for two weeks total. This is both so that the flavor can develop and so that the yeast and other material, such as hops, can settle out and you can have a lovely, clear, refreshing beer.