It's real simple to cook fresh beets. 

Cut tops off leaving 3-4 inches of the stem on the beets 
and don't trim the root end.
 
Wash and drop into a large pot of boiling water. 

Cook on medium heat just until tender when pierced with 
a fork (cooking time depends on the size, try to get them close to the same size). 

Drain and put into ice water for about 5 mins (this cools 
them down quickly and stops the cooking process).
 
Once they are cool enough to handle, just use a knife to slip the skins right off. 

Trim the stem off and cut off the root end......VOILA!! 

Patty