My brother has a black eye and a lot of blood in the white of his eye from being punched. How can I help?

Eye exam. Need to rule out other ocular injuries including any orbital fractures. If the vision is good, no eye pressure problems, and the eye itself is intact, then blood should resolve without issue.
See an eye doctor. The best thing you can do for him is to rest the eye and have him sit upright. He may have a hyphema or bleeding in the eye and his eye pressure may be elevated. He needs an eye exam by an ophthalmologist to rule out anything more serious.