Check the physical makeup of the slope where you intend to plant. Some slopes are simply too steep. A good rule of thumb is that you should be able to roll a wheelbarrow directly up the slope if you intend to plant it with grass.
Dig several small holes over the area of the slope. If the soil is only a thin covering over rock, it is likely to erode with rain. Make sure there is a good soil base. Grass actually encourages erosion, so a solid soil layer of at least a few inches is essential to slope planting.
Scatter fertilizer over the area you intend to plant once you have satisfied yourself that it is a good area for grass planting. Rake the fertilizer in to blend it with the first inch or two of soil.
Scatter seed evenly over the entire area.
Water the slope very lightly, no more than an ounce per square foot.
Cover the entire area with straw matting, which will help the grass seed hold in place while it takes root and begins to grow. Once the matting is in place, you can water the grass a normal amount for the duration of the growth.