From Shaving Made Easy, a book in the public domain I like to recommend to shavers new and old:
To make the lather, see that the soap is placed in the cup according to previous directions. Fill the cup with water, allowing it to stand for a few seconds, then pour the water out. Usually sufficient water to make the lather will adhere to the cup, soap and brush. Now with the brush, mix thoroughly, using a combined stirring and churning motion, until a good thick lather appears. The more the brush is rubbed over the soap the thicker the lather becomes. A great deal depends upon having the lather just right. If it is thin and watery, you will have poor success in shaving. The more creamy it is, the better will be the effect of the alkali in stiffening the beard. Some of the poorer qualities of soap produce lather very quickly, sometimes half filling the cup, but it will be found thin and without lasting qualities, so that by the time one side of the face has been shaved, the lather is all gone from the other. A good soap will produce a thick creamy lather that will last throughout the entire process of shaving.
Applying the Lather.
Put the lather on with the brush, covering every part of the face that you intend to shave. Then with the fingers rub it thoroughly into the beard until the lather has had sufficient time to stiffen the hairs. Next to having the razor in perfect condition, this is the most important thing to do; for it is impossible to shave easily unless the face is well lathered and the lather thoroughly worked into the beard. Go over the face once more with the brush, in order to spread the lather evenly, and then begin shaving at once, before the lather has time to dry. Should it dry while you are shaving, wet the brush slightly and apply fresh lather. If you prepare your face in accordance with these instructions, a keen razor will slip over the face so easily that shaving will become a real pleasure.