Pick a good time to do the job. Avoid days when the chance of heavy weather could mar your finish while the paint is drying. Cover the deck the night before the job to keep it clean and dry. Clear the deck of all items, and scrape off all loose material. Anything that is loose on the deck is going to be a weak substrate, and eventually it will come off, taking your nice paint finish with it. Use a scraper or similar tool. Patch any holes or cracks, using an epoxy patch or similar product, and sand off rough areas.
Begin with a latex primer, since you will use latex paint. The primer is an important part of the process ,so don't skip it or just use an extra coat of latex. The primer might not look like much, but it will form a surface and bond with the paint. Apply the primer with a roller, using a brush for tight areas. Investing in a painting pole to use with the roller is a good idea, especially if you are covering a large area; it will spare you back and knee pain from bending over or working on the ground.
Once the primer is thoroughly dry, apply the latex paint, again with a roller or brush. Two or more thin coats are preferable to one thick one, as a single, heavy coat might not dry uniformly. Also, if you miss a spot on the first pass, you can cover it on the next coat. Some deck paints have granulation to improve footing, so shake the can well. Follow instructions carefully to ensure the best adhesion and take full advantage of the safety features of the paint.