Backyard Drainage Problem Against House
We have a 1920's home in Seattle Wa, where it rains often. The previous owners built an open shed off of the back of the house to take the water away out into the grass area when it rains. The shed has a cement slab and cement stairs off to one side down into the basement. The shed is rotting and has an abundance of holes in the roof, so we would like to tear it down. This would gives more space in the backyard to plant grass, and put a patio.
The issue is, if we tear down the shed, the rain will fall right up against the house and rainwater will run off of the backyard, which has a slight slope and run straight up against the house, into the basement. Ultimately we would like to void the cement slab after the shed is down.
Is there something we could do for drainage. I have a few ideas, but don't know how to get started. Do I take a jack hammer to the cement, then dig a trench for a French drain?