What is lather? How does it work? How do you make it? Those are regular questions that are often asked. Lather is a mixture of air, water, and either a soap, other surfactant or a soap-like substance. The lather lubricates, hydrates and protects the face from irritation and nicks when shaving. Making proper lather requires water, a shaving soap or a shaving cream product and a shaving brush. Depending if you want to face lather or bowl lather, you might require a small bowl or mug.
Getting started with lather
Lather must provide slip for your razor, and cushion and protect your face. Properly hydrated lather is critical, but overly wet lather will get bubbly and won't provide much cushion or protection. One trap is that fluffy, rich lather can be too dry. You aren't necessarily going to get the same lather you get from an aerosol can of shaving foam. Start with a dry lather and add water until it behaves the way you want. You can also have a look at The New Guys Guide to Inexpensive Soaps and Creams.
Bowl, face, or palm?
There are different ways to create lather and each way will provide the desired result: Lather. See this page for more information.
The lather's sweet spot
The first time you use a new cream: shake the brush 4 or 5 times. Get an almond size dollop (sometimes called a "snurdle") of cream and wipe it in the breech of the brush. Whip the lather for at least 30-45 seconds (like you're beating eggs) and see what the lather looks and feels like. Take a little between two fingers and feel it. Now add about half a teaspoon of water and whip another 30 seconds or so. Continue doing this over and over, feeling the cream each time and paying attention to what it looks like and feels like when you're whipping it. Continue doing this until the lather is obviously over saturated (very thin, large bubbles, won't support itself in a peak, etc.).
Now repeat the whole procedure with the same cream. The "sweet spot" ratio will stay the same, and after a few bowls you'll recognize when the lather is at that sweet spot and at its most lubricating. After 5 or 6 bowls you shouldn't have any problem getting it "sweet" without much hassle.
Note that some soaps and creams require the water to be added slowly, rather than all at once (even if the total amount ends up the same). Also, you may find that you need to add a small amount of hot water to the lather as the shave progresses.
Once you have a rich, thick, and lubricating lather, begin lathering up your face. Some people prefer rubbing it on in circles, others prefer painting it on. Stiffer brushes lend themselves more to circles, while softer ones seem better able to paint. Whatever technique you use, spend more time applying the lather than you think you should. Doing so results in better saturation and also helps the whiskers to stand up better.