Goats need some form of shelter to get out of severe weather. The shelter does not have to be fancy, or even completely enclosed. It needs to prevent drafts in cold weather and allow the goats to stay dry in wet weather. It only needs to be large enough for them to lay down in comfortably in severe weather. A run-in shed fits the bill perfectly. It will keep your goats happy and is easy and cheap to build.
Plan the size of your shed. Your run-in can be as big or as small as you need depending on how many goats you have. Each goat should have at least 4 square feet of space in the shed, so 15 goats would need 60 square feet of floor space. An 8 x 8 foot shed will comfortably house 15 goats. Of course, the more floor space per animal the better. This plan builds an 8x8 run-in, but is easy to modify and make longer.
Clear a spot. Your shed should be on level ground to give it maximum stability. Dig corner post holes to a depth of at least 4 feet. The depth is especially important in areas where ground freezes in the winter. Weather-related freeze and thaw would cause a structure to buckle if the supports are not deep enough.
Cut two 4x4 corner posts to 9-foot lengths for the back corners. You will bury 4 feet and the remaining 5 feet will be above ground. Leave the remaining three posts at their original length. You will bury 4 feet and the remaining 6 feet will be above ground. This gives your roof enough slant for water to run off, and for snow to fall off, in the winter.
Plant 4x4 corner posts in the holes you open. For extra stability, you can pour quick set concrete into the holes around the posts. Use a level to make sure the posts are straight. Backfill the holes around the posts and pack firmly.
Dig a post hole halfway between the two front corner posts for a door opening. Plant a 6' post in the opening. Use a level to make sure it is straight, backfill and plant firmly.
Attach 8 foot 2x4 slats from corner to corner at the ground, the middle and the top of the wall areas except for the front. Cut the 2x4 slats for the front to only cover one half of the opening from door post to corner post, leaving a 4-foot opening to enter and exit the structure.
Attach one 10 foot 2x4 slat to the left front corner post and the left rear corner post, and one 2x4 slat to the right front corner post and the right rear corner post. Attach an 8' 2x4 slat from side to side across the rear and front of the roof from side to side.
Attach plywood to sides and roof. Cover roof with shingles if desired to weatherproof the shed. Paint with sealer to protect the wood. Use barn paint that is safe to use around animals.