First thing to figure out if it is blocked. Trying to clean out a drain pipe that isn't blocked is a fools errand. Remove the downspout and place a hose in the opening. Turn on the water. If it backs up and comes out of the hole, the drain is blocked. Now you can proceed to figure out why.
Drainage systems run to either a sewer system, drain outlet or to a dry well. Many of the Everett drainage systems where we live run to a drain outlet. You will not be able to access the far end if it is a sewer system outlet.
If there is a drain outlet it will likely have a drain screen on the end. Remove the drain screen and remove any debris blocking it. If you cannot find the drain outlet, remember that it will be at a lower elevation than the inlet. Try putting high strength dye into the drain pipe and running water through it. Use an entire bottle or septic dye tabs. Look for the dyed water coming out.
If the drain system is still blocked, get a plumbers auger. Do NOT use a power auger. Power augers can damage a drain system like this that is most likely made out of pvc pipe. Manual augers are available up to 75'.
Start at the inlet side and run the auger until it hits a blockage and cannot be pushed forward. Flush the pipe with water and snake it again. Continue until the blockage is gone, you cannot push the snake forward any more or the snake length is exhausted.
If the snake length is exhausted, run the snake back from the far end of the pipe and repeat the process until the blockage is gone.
If the snake hits an immovable blockage, the pipe will need to be dug up. Run the snake into the pipe as far as it will go. Get or rent a metal detector and follow the snake down the yard until you reach the end of the snake where the blockage is. Now you know where the blockage is. The blockage may be caused by simple debris but it is likely to have been caused by a truck driving over it and crushing it or tree roots intruding on it.
In any case, dig up the pipe and this point and remove a section of the pipe to eliminate the blockage. Replace the pipe section with a new section. Test the drainage system for proper flow by running water down the drainage system.
If the pipe is still blocked repeat the auger process.
Many times if this does not fix the problem you will ultimately find out that the problem is most likely being caused by a blocked dry well. Dig up the dry well and replace it per the manufacturers instructions.
Finally, if you fix your problem and you found the exit port for the drain system, mark the location so that you can find it again. Make certain that the drainage system downspouts have debris blockage screens. Our home's Everett drainage system is tight with leaf guards on the gutters, screens on the downspouts and screens at the entry point into the underground system. While this approach requires regular maintenance it saves us from having to dig up the yard!