The following online articles will help you get starte but you may find that this is best left to a drainage or excavating contractor. But prices range from to depending on the size of the well, the labor involve and the materials used. With a long-handled shovel, tunnel under the sidewalk and dig a trench foot deep and inches wide that slopes gradually toward the hole.
Coming out from the downspout, at least feet from the foundation (and feet from any property line dig a hole about feet deep and wide. Gallon Barrel Dry Well: I had a section of my backyard that turned into a river during heavy rain.
This is a means of stormwater management that works well for relatively small volumes of storm water runoff in a location where the groundwater table is low enough so that the bottom of the dry well can remain at least feet above the groundwater table. Then the water pooled for a while less than feet from my house and finally made its way along the path of least resistance into my ter listening to the advi.