Start by pouring five gallons of juice into a glass carboy. You can use fresh squeezed juice or store bought juice. I sometimes like to mix my own flavor. It's ok to use 4.5 gallons of apple juice and .5 gallons of something else you think will perk up the flavor. Experiment!
Once the juice is in the carboy you are ready for the yeast. You have several choices. You can use a champagne yeast if you want a dry product that does not retain apple flavor, you can use dry beer yeast if you want it to remain somewhat sweet and still have a hint of apple flavor, or you can pickup a special liquid yeast intended just for making hard cider. I use dry beer yeast.
Now put a $1.50 airlock on top and fill it with vodka as a barrier to bacteria or wild yeast falling in. Place the carboy in a reasonably cool and dark place, such as a closet, and leave it there for two weeks. You should see bubbles in the airlock within 24 hours. After two weeks siphon the hard cider into a second carboy and again leave it there for two weeks. At this point you should have no activity in the airlock and the cider should look very clear.
You last step is to bottle the cider. You can use old, but clean, beer bottles for this purpose. Soak the bottles in an iodine solution (instructions on the bottle) to make sure they are sanitary. Use a siphon hose with a crimp to feel each bottle from the bottom and then cap them. I prefer a bench capper (vs a wing capper) which can be had for about $50.
Once again, leave the cider alone for two weeks or slightly longer. Refrigerate and start enjoying them. You should be able to make a very enjoyable product this way but there are a few extra things you can do to alter your cider.
One of the most popular things you can do is add some additional sugar to increase the alcohol content. Using apple juice from the store you will start with about 5-6% alcohol once it is fermented so any added sugar will add a punch. The most common types to add are corn sugar or honey. When I make my cider I heat up 3 pounds of honey on the stove so it is very viscous and pour it in with the cider. If you are using a 5 gallon carboy you may need to decrease the amount of juice you use to accommodate the honey.
In a quick nutshell that is how to make hard cider. It is a very refreshing drink in the summer and I've found it to be very popular with friends and family. So get cracking because summer is coming up fast.