The first thing you need to do is clean/degrease the screen. Wet the mesh, and sprinkle either some trisodium phosphate, or some dishwasher detergent on the screen. Scrub lightly with a nylon bristled brush like you use to clean dishes. Rinse throughly, and allow to dry.
Next, you are going to coat the screen with photo emulsion. There are different brands, but I use Speedball, because it what I have used, and it is easily available to me at my local art supply store. The photo emulsion comes in two parts, the emulsion, and the sensitizer. The sensitizer comes in a small bottle, to which you will add a little bit of tap water. You shake it up real good, then mix it into the larger jar of emulsion, then mix well. Sensitized photo emulsion has a limited shelf life, but can last for months if kept in the refridgerator.
You can coat a screen without a scoop coater (a small handheld aluminum trough), but I highly recommend making the investment in buying a scoop coater. I bought mine for about $14. With a scoop coater, you save time, and coat the screens much more evenly, giving you better prints.
Without a scoop coater, pour a thick bead of sensitized emulsion at one end of the screen. Now using the squeegee, spread the emulsion across the screen. Keep doing this on both sides until screen is evenly coated. You may need to add more emulsion, or have to pour some back into jar. Make final squeegee pass on inside of screen.
With a scoop coater, pour some emulsion into the coater.
Hold the screen at about 45 degrees, bottom side down. Place the loaded coater against the bottom of the screen. Tilt the coater so the emulsion flows to screen. Now with a smooth slow motion, pull the coater up to the top of the screen.
While continuing to hold the coater against the screen, tilt the screen 45 degrees away from you so that the emulsion flows back into the coater, then pull the coater away from the screen. You should now have a nice evenly coated screen.
Now you need to dry your screen. Take some push pins, and push them into the wood in the corners on the bottom side of the screen. Alternately, you can tape about 5 pennies to the bottom side of each corner. The object is to be able to lay screem down to dry without the wet screen to be making contact with anything. Place the screen to dry in a dark place, bottom side down. The screen needs to be horizontal when drying.
If you are a professional, you will probably want to pour the emulsion left over in the coater out, as it may be contaminated. I am am not a professional, I am a hobbyist and am printing on a budget, and have not had a problem. I pour the left over emulsion back into the jar. I find using a spatula helpful. Close the jar, and store in your refridgerator.
Wash off the coater, spatula, and whatever else with warm water.