Survey your hillside to get a sense of the slope incline, runoff areas, and spot where water might pool. Examine the consistency of the soil to get an idea of how readily it will absorb rainwater, and whether it contains rocks that might come loose. You should also ascertain what kinds of plants the soil will support, especially any plants native to your local environment.
Chart out a location for a gutter system at the bottom of your hillside, which can collect the water from your runoffs and take it safely off your property. Make sure it adheres to all local building codes and doesn't cross over into your neighbor's properties.
Set up runoff areas and drainage control systems leading down the hill. In some cases, you can do this with traditional gutter systems or naturalistic stream beds. In other cases, you may wish to install underground drainage pipes to collect water as the soil absorbs it. The specifics vary depending on the exact layout of your land.
Identify pooling areas and either fill them with rocks or sculpt them to permit water to runoff. If water is allowed to pool in a single location, it will erode the surrounding soil and increase the chances of a mud slide.
Plant along the hillside a densely packed cover that can repel water instead of absorbing it. Grass and sod make good basic cover, as do any plants with deep or extensive root systems. Plants that grow naturally in your area are especially reliable, since they can naturally withstand local weather conditions and thrive without a lot of care. Matting, mulch or even just plastic tarps will do in situations where you cannot plant.
Inspect your hillside every six months or so -- right before and right after the rainy season -- to check for damage and identify possible problem areas. Call a landscaper if you note a spot that needs repair.