The most basic method to manage downspout water is with downspout extenders. These are plastic tubes or angled concrete pads that direct the water further from the home. The minimum distance a downspout should terminate is four feet from the foundation. This depends on the lot grading around the house. The water needs to exit in a location where the grade is sloped well away from the building.
City Sewer System
On older homes the roof's downspout system terminates below the house and into the main drain for the house. This moves the water into the city's sewer system. When the system works properly, it is effective because the moisture is 100 percent removed from your property. An issue arises when the main drain under the basement gets clogged with debris. This can lead to the flooding of your basement with rainwater. Some municipalities have since banned this practice, so consult your local building authority before going in this direction.
A French drain is a gravel filled hole which the downspouts feed into with underground four-inch ABS piping. The gravel fills with water and provides adequate area for the water to leach into the soil. A properly built French drain is at least 15 feet from the house and is large enough to manage the volume of water your roof generates. The size of the French drain depends on your drainage qualities of your soil, size of your roof and approximate volume of water during the worst yearly rainfall. In areas which see freezing temperatures, the French drain must be designed to withstand the forces of frost.
A swale is a lot grading detail which moves the water into a low spot at least 10 feet from the home, then away from your property. They are typically used where the natural slope of the ground is towards the building. Swales are made by using an excavator to modify the grade around your property. One dilemma is where to move the water to. Most local building authorities require you to manage your property's water in a manner that doesn't affect you neighbors' land.