Boats to the airstrip on Manda Island (KSh100) leave from the main jetty about an hour before the flights leave. In theory, you have to be at the airport an hour before your flight.
Plenty of motorised dhows run to Shela throughout the day until around sunset from the new jetty; these cost about KSh100 per person if you share a boat with others or KSh500 if you don't. After dark, boat captains charge KSh1500 between Lamu Town and Shela.
There are also daily boats between Lamu and Paté Island (KSh200 to KSh250, two hours).