Classic egg tempera technique starts with a detailed drawing on the panel. It is recommended to use fine charcoal or a silverpoint stylus rather than pencil, since graphite has a tendency to work through paint layers.
Then, paint over the drawing with ink. If you use water-based ink, you must have a very light touch with the first layer of egg tempera you put over it or the paint will dissolve the ink. After the first layer the tempera acts as a waterproof barrier and the ink is protected. The underdrawing is so you will have a strong sense of the image and its lights and shadows before you start.
But even in the Renaissance this technique wasn't always followed. There is, in the Metropolitan Museum of Art in New York, a beautiful English painting of two saints flanking the Madonna and Child. The Madonna was obliterated and a posthumous wedding portrait of Henry VII was painted over it. When this spurious image was removed, the loose underdrawing of the Madonna was revealed. It is recognizable, but very far from the precise underdrawing said to be the only classical way. Really, any way of starting a painting that you are comfortable with will do, as long as the paint is laid on thinly.
Egg tempera paint should be painted thinly. Impastos will crack. Beyond that, you can do a lot. Sponging, spattering, crosshatching, washes, glazes, scumbling, even airbrushing is possible. Egg tempera dries within a few minutes when painted thinly. If you lay out very wet washes it will take longer.
If you go over the same spot with too much water, or if you go over a spot several times before it's really dry, you may pick up the underlayers of paint all the way to the gesso. DON'T PANIC. Let the marred spot dry -- it will only take a few minutes, so be patient. Then, very lightly and with almost a dry brush, dot in thin layers of color to blend with the paint around it.
After a week, egg tempera will be dry enough to paint over with some vigor. But, after a few months you will be hard pressed to budge the underpainting. These are just some beginning tips and techniques for egg tempera if you are further interested you can find out more online or at any large art supply store.