How many downspouts?
The rule of thumb is one square inch of downspout for every 100 square feet of roof. A standard 2x3" downspout (6 sq in) handles about 600 sq ft of roof, and a 3x4" downspout about 1,200 sq ft. Use the actual sloped roof area, not the footprint: a steeper roof catches more rain. In areas with heavy downpours, plan on about a third less roof per downspout.
5" or 6" gutters?
5" K-style gutters with 2x3 downspouts suit most houses. Step up to 6" gutters with 3x4 downspouts for steep roofs (8/12 and up), large roof areas draining to one run, or places with intense storms — they also clog less with leaves.
Where downspouts go
Put a downspout at the low end of every run. Runs longer than about 40 ft get one at each end, with the gutter sloped from a high point in the middle toward both. Avoid putting a downspout where it will dump onto a walkway or driveway.
Slope and hangers
Pitch gutters about 1/4" for every 10 ft of run toward the downspout — enough to drain, but not so much that it looks crooked. Fasten hidden hangers every 24" into the rafter tails or fascia, or every 18" where snow and ice load the gutters.
Move the water away
The building code calls for roof water to discharge at least a short distance from the foundation, and most builders recommend 4–6 ft. Use splash blocks, downspout extensions, or a buried pipe to a drain or dry well.
Sources: University of Illinois — gutter and downspout sizing. Water still pooling? Plan a French drain.