You happened to ask a good person — I grew up near Foster Lake and my family used to walk on the shoreline trail every evening! The walking trails at Foster Lake are great, and there are lots of places where you can walk right up to the lake shore and dip your toes in the water. However, they do not extend all the way around the reservoir.
The north shore trail begins at Lewis Creek County Park, which is located off of North River Drive.
On the south shore, the walking trail begins at Shea Point (just off Highway 20, across from the spot where Riggs Hill Road intersects with Highway 20) and extends up to the far edge of the dam.
If you visit the Sweet Home Chamber of Commerce website and scroll to the bottom of their list of local trails, you’ll find a good description of both the North Shore and South Shore trails.
If you visit Foster, stop and get a bite at the Point Restaurant. It’s right across from the South Shore trail and has good food plus beautiful lake views. It’s especially known for its homemade pies — yum!