Build simple terraces. It will help hold in the soil and water, but retain the character of the hillside.

I love my terraced beds. You can put up a board, bang in some stakes to hold it in place, and put improved soil behind it for planting your tomatoes. Start with a few beds this year and expand. Just make sure you always have good places to set your feet!

Here is a link that might be useful: my website

The above suggestions are good. The steepness has a lot to do with how dramatic a solution you will need. You will want to slow down the velocity of flowing water. A relatively simple barrier to slow the velocity of flowing water is to place logs in very shallow trenches (just deep enough to keep the logs from rolling down your hill) and also secured with stakes. There are also lots of fancy products you can buy if necessary.

My vegies are on a 45degree slope. When my house was put in the leach field was put in about 8 to 10 feet below and the fill was just as it was dozed and fell to the lower level. Last year I decided I wanted a few Toms and Peppers 18 each LOL but nowheres to put them where they would get much sun except the hillside.
My answer lottsa stones from an old wall. Carry up the hill and terrace then fill in it gave me 2 to 4 feet by 60. This year its harder the carry is getting longer on my 2nd tier. Now I have to wheel the fill down the hill to the leach field shovel into 5 gallon buckets climb up on the 1st tier dump ugh. I have room for 4 or 5 tiers but at least by next year I should be able to put a temp ramp from the side hill and eliminate the shovel bucket routine. You got good answers from the others for the easiest fixes but this post is just to show no slope is to steep.
Regards Scott

My house sits atop a Knoll, Property is full of shale rock and goes downward slope. Like others you can become very inventive as to how to terrace little areas on your "hill". One of my favorite is to reuse cereal boxes, oatmeal boxes, catfood boxes (you get the idea) Dig a hole put a little miracle grow soil in container than plant the plant or shrub, fill remainder up with soil. I use a lot of newspaper around my plants in the beginning to keep water and soil from running off. Box eventually deteriorates In time I might cover the newspaper with bark mulch, cut grass clippings, or whatever. Has worked very well for me. made for some very nice soil-----also can add ground cover if you are planting perinnels, myrtle is a fast grower and vinca puts out a lavender flower in my zone 5. Good Luck