It seems to happen the same way every time -- your edger was running fine when you put it away for the season. However, now it's spring, and after about the tenth yank on the cord, irritation kicks in -- you realize you won't be edging today -- it's just not going to start.
Failing to Start
Three of the most common reasons an edger will not start are old fuel, the switch in "Off" position or a flooded carburetor. The first two are easy to solve -- replace any fuel in tank with fresh fuel and double-check that the switch is on. If your edger is flooded -- which can be determined by an excessive odor of fuel -- turn the switch to "Off," pull the cord five or six times, and then turn switch to "On" and start.
How to Troubleshoot
If your edger is not flooded, you need to troubleshoot. Since you have already added fresh fuel to the tank, make sure it is flowing correctly. First, follow the fuel line from the gas tank to the carburetor and make sure the line is not split, cracked or kinked. If it is, replace the line. If the line is okay, check for a dirty fuel filter, which is normally in bottom of fuel tank, and if dirty, replace it. If edger still does not start, you need to look at two more things.
Filter and Plug
Remove the air filter from its housing and wash it thoroughly with soap and water. Once filter is clean and dry, put a drop or two of oil on it, squeeze the filter to distribute oil, and then reinstall. Pull the cord. Success? If not, move on to the spark plug. You can test a spark plug to make sure it is working, but since they are relatively inexpensive, it is easier to replace them. To replace, remove the spark plug boot and spark plug. Before installing the new one, set spark plug gap to .025 inches. If the edger still doesn't start, you may have a low compression issue -- which a professional would need to repair.
Ounce of Prevention
All engines benefit from regular scheduled maintenance, and a good practice is to perform maintenance on the engine in the fall before you put it away for the season. Each fall, replace the air filter and the spark plug. Drain the fuel tank completely before storing the edger for the winter. Dispose of any leftover fuel in a gas storage can and add a fuel stabilizer to the can.