All animals have an instinct to find shelter in inclement weather, and goats are no exception. They don't require an elaborate set-up, unless you want to build one. Goats can get pneumonia if they are wet and cold, and pneumonia can be fatal for goats.
Consider the climate to determine the type of shelter to build.
Decide how big the shelter should be, depending on the number of goats you have. Consider at least 10 square feet for as many as three goats, and larger if you will breed them or get more goats.
Find a location for the shelter. Choose high, flat ground that won't flood. The back of the shelter should face the wind, so your goats have protection from drafts.
Determine your budget.
Dig four holes for the corner posts. The holes should be at least 3 feet deep.
Insert the posts in the holes and reinforce them with concrete. Let the concrete dry around the posts, then add dirt, and pack the dirt tightly.
Build the three sides with sturdy 2-by-4 boards. Use at least three boards for each side, spacing them evenly. Use at least four nails for each end of the boards: two on one side and two on the other.
Build the roof from thick plywood and shingles or tin. Tin will be quicker and cheaper, but may not be as aesthetically pleasing.
Nail thick plywood boards to the inside of the shelter to prevent the goats from climbing and provide extra protection from the elements.
Add bedding to the floor of the shelter. Straw and/or pine shavings work well.
Consider buying a pre-made shed or large doghouse. If you plan to breed your goats, consider sectioning off an area or designating a stall for the mother and kids.
Goats do not like to get wet. If your goats are exposed to wind and rain and cannot find shelter, they can become sick very quickly.