The easiest way to begin assessment is to remove the inner part of the dome above the shower which will allow you to see the structure between the two dome shells (the wood beams, etc.). Usually attached with about 4 to 6 screws. You may find wet &/or rotted wood and it might show you exactly where the leak is. If it is still wet, leave the inner part of the dome off to air dry. Until you see what's up there you won't know how much of a job it will be. Most importantly...be sure after any repairs are made the outer dome is sealed very well. Good luck!