Congratulations on your new home. It is true that runoff that is improperly channeled will cause damage and devaluation of your property. The first thing you can do is during the next rainfall, watch to see where the runoff comes from and its path. Watch to see where the water flows and where it exits. Ideally, your home will have sufficient outlets to handle rainwater runoff. If not, then let us come out and conduct our 10 point inspection.
This is a common problem for homes where the grade less than 1%. An ideal grade in a yard is one that slopes away from the house. Slightly regrading the garden and installing a sump pump is a relatively easy and sure fire fix.
This is common with homes collecting litter beneath the under story of tall trees. Debris removal and regular maintenance of gutters is necessary to discourage nesting. Adding screens to gutters also keeps debris out of drainage systems.
Improperly installed downspouts leave standing water which can cause foundation problems and allow mold to grow. A downspout must direct rainwater away from the house and ideally into an underground drainage system.
Erosion from higher elevation runoff is a serious problem faced by home owners in the Berkeley Hills. There are a few things you can do to slow the water, including terracing, re-vegetation, and building swales to direct runoff to an underground drainage system.