Consult with the local building department. While a swale is technically a landscaping project, strict rules regulate how and where excess water leaves the property.
In nearly all municipalities, you are not allowed to divert runoff onto your neighbor's property.
Discuss your project with your neighbor if the swale must run between the houses. If your neighbor also needs to divert water from his foundation, he may join in on the project -- or at least allow you to dig on his side of the property line.
Dig a V-shaped trench from the low spot in the yard out to the gutter or drains. Generally a swale does not have to be more than 6 to 12 inches deep and 2 to 3 feet wide.
Slope the sides gently to the bottom of the swale and toward the street. Use a level to ensure that the swale slopes away from the house foundation.
Rake the sides and bottom of the swale smooth. Use the level to ensure that the swale slopes toward the appropriate drainage.
Roll the sod over the bare soil. Fit the edges tightly together, then run a sod roller over the swale, pressing the new sod into the soil.
Water frequently until the new grass is established.