Clean the swing set thoroughly to remove any dirt from the wood. A power washer works well for this purpose, but you can also use a garden hose and a rag to clean away visible dirt.
Sand the swing set to remove any rough surfaces or old flaking paint. Existing paint on the swing set could prevent the stain from adhering properly, so sand it away and wipe away any dust created during sanding with a clean rag.
Apply an exterior wood stain to the swing set with a paint brush. Look for a stain that provides UV protection and water protection to extend the life of your swing set.
Allow the stain to dry completely before you allow children to play on the swing set.