This is how I've done it.
Wash and prepare as described by ElizabethK. Push the cuticles back, optionally cutting off any excess using an appropriate tool. Remove any left-over residue from the nail surface using a diagonally cut orange stick lightly wrapped in cotton (or some other implement that you find safe and convenient).
If your nails are strong and thick it's possible to smooth the surface using e.g. very fine sandpaper or file and a buffer. Mine aren't, so I don't.
The layer of base coat also functions to smooth the surface and protects the nails from absorbing color. Just before brushing on the base coat I like to dehydrate the surface of the nail using e.g. 190 proof alcohol or pure acetone.
Adjust the amount of polish on the brush by lightly touching the side that will face away from the nail to the rim of the bottle as you pull it out.
One stroke is enough to cover very narrow nails. On the average expect to use two or three strokes. To start each stroke place the brush close to the base of the nail, at a high enough angle and far enough from to the cuticle to be able to by lightly pressing down fan out the brush tip to fit the cuticle curve. Then smoothly pull the brush all the way to the tip without stopping. Most nails will probably need at least two strokes, one along each edge of the nail. If two strokes don't cover the entire nail, make a third stroke to cover the gap in the middle.
After the last stroke of each layer I also usually run the brush lightly along the cut edge of the nail tip without adding polish. It seems to reduce chipping.
If the brush happens to touch the cuticle, break the bridge of polish formed by running e.g. a toothpick, a sharp cotton bud or something else convenient on the nail along the cuticle edge. This should leave a clear line. Don't worry about entirely cleaning the area at this point. If a clear line exists, you can clean up later. If it doesn't, the polish layer may be too thick so try using a bit less manicure.
Once the base layer is dry enough to no longer be tacky or soft to the touch, brush on the color. To do this repeat the procedure above, making each stroke motion smoothly and fast enough to not melt the previous layer(s).
The first color layer should cover the entire base layer just to the edge of the cuticle. Again, if you do happen to touch the brush to the cuticle, break the bridge as described above.
The second color layer functions to fill out and even the color. It's best to concentrate on making it smooth rather than on placing it as close to the cuticle as possible. It can also be a bit thicker, if necessary. (Good quality polish usually gives better color coverage than very cheap ones).
Once the color layers are dry you can apply a clear top coat to increase gloss and strength.
If you did happen to get polish on a cuticle, remove it now using e.g. a cotton bud moistened with remover, or any other method you find convenient.
Remember that the polish will take some time to fully cure even after it feels dry. If you for example go to bed soon after doing your nails, you may wake up in the morning with the weave pattern of your sheets embossed on them.
I hope this is of some help.