Often, when a homeowner tries to clean their screens, the idea is usually quickly discarded after the screens begin looking worse than when the homeowner began. You know, irregular lines where the hose sprayed, patchy & splotchy marks that will not come off. Living in the Arizona desert like we do, there is often a huge demand for this service, and although we use a special (and expensive) chemical that cleans and seals the screen fabric from dry rotting and attracting dirt, there is a way for the typical homeowner to t least clean their own screens.
So the question is:
How do you take screens that looks like this:
And make them look new again, like this:

The answer is this:
First you get some liquid Tide with bleach alternative:

Then you put roughly 4 gallons of water in a 5 gallon bucket. Next, add one capful of the aforementioned tide and mix.
You will also need a stack of terry towels:

Terry towels can be purchased in bags of 25 very inexpensively at Costo, WalMart, or in the car cleaning section of any auto parts chain (ie, Checker Auto Parts, Auto Zone, etc). The towels will be getting quite dirty in most cases and if you opt to use towels that you use regularly in your home, be prepared to have dirt stains that may not come out.

Get a kitchen broom (probably not the one you would want to actually use in the kitchen again... I've never tested the ability to wash out the broom for regular use, although I'm pretty sure it would be okay...) and put the bristles down into the bucket.
Next, stack all of your screens in the drive way laying down flat. With some force, agitate the top screen with the broom, scrubbing it well, evenly spreading the soap and water mixture all over the screen. Once the screen is covered in soap and has been vigorously scrubbed, dipping the broom as many times as necessary to saturate it, flip the top screen over (and notice that the soap mixture is draining down onto the screens underneath to that you won't have to dip the broom as much for the subsequent screens). Now repeat the scrubbing technique for the other side of the screen.
Once the screen has been coated and scrubbed well, hold the screen in both hands and gently (yet firmly) slap one flat edge of the screen on the ground, allowing a good amount of the suds to fall to the ground, probably looking quite dirty... the idea here is that you lifted the dirt off of the screen with the soap during the agitation process and now the majority, if not all, of the dirt is now inside the suds. When you slap the screen on the ground, you are removing quite a bit of the dirt just by sending the heavy suds down to the ground.
There will still be a large amount of suds on the screen, so you will now lean the screen against the garage door and systematically "flick" the screen (you know, locker room style) with a clean, dry terry towel. You will be sending the remaining suds flying onto the garage door and the ground below the screen. Zig Zag down the screen making sure that you are getting the bulk of the soap off, but understand you are only trying to get about 90-95% of the soap off this way. You will spend forever trying to get all of the soap off, besides, you want to have a little left for the final polish.
You will notice that the towel will get saturated in the corner that is doing the "flicking" and will begin to lose it's effectiveness. Change "flicking corners" of the towel as necessary in order to maintain efficiency, and also to keep from leaving marks on the screen from heavily soiled corners.
After you have finished "flicking" you now take a reasonably dry towel (probably the one used for flicking if it's not too wet) and use it to wipe down the screens frame, which is probably quite wet still. After wiping the frame, you may need to get a new towel, but if it is stillreasonablydry, fold it in quarters, exposing the cleanest section of the towel as the wiping surface. Systematically wipe the entire screen for the final polish with a zig zag motion again, and notice that any water or suds that was on the screen will easily come right off in this stage. The screens will look perfect after this 90% of the time. If not, they were probably very dirty or not scrubbed well enough, but a second time through will do the trick.
A few important notes:
Screens are pretty delicate by nature. You need to be sure to not slap them on the ground too hard. Particularly if the corners are made out of plastic.
Also, when agitating the screen, be sure not to put too much pressure on the screen that results in pressure that wants to pull the screen out of the frame. This will cause the screens to look "saggy". The reason I recommended laying them flat on the driveway is because that allows you to put a good amount of pressure on the screen as you scrub, without pushing the screen out of the frame. As the stack gets taller, you may notice that there is enough airspace to cause it to be possible to get the undesired effect of pulling the screen away from the frame. If that's the case, make sure to decrease the size of the stack by breaking it into 2 or 3 stacks.
It should also be noted that this method will work only on "Bug" screens. If you have "Sun Screens" or "Solar Screens" which usually cover the entire window and are made of much heavier screen material to shade the building's interior like this:

You will need to do the same thing as far as cleaner and brooms go, but instead of "slapping" and "flicking" the screens, you will need to use a garden hose with a trigger that allows a "flat" or "fan" spray and rinse it off in straight line passes and allow them to dry well before re-installing them. You may need to repeat the process numerous times for perfect results (Sun Screens usually hold a lot of dirt and cling quite vigorously to it!), but it is possible.
Also, this method is for cleaning, and does not include the professional sealing process, but you will find that if you clean your screens every 6 months, you can achieve a similar result.
Even though I'm sure that I don't need to point it out, but I will anyway...
A screen that looks like this:

Which is rotting from the sun, getting saggy, and is quiteliableto tear, should not be cleaned as it will only do more damage, and certainly will not improve it's look or add any life. Kind of like a torn up or damaged shirt... throwing it in the washing machine is not going to bring it back to new.
I think that's it. Contact me or leave a comment if you have any questions... I know this was long!