Local and state roads connect most parts of the mainland portion of the park, so cars or bicycles are the most practical way of getting from one to another. One potentially confusing road is M-22, which goes up the west side of the Leelanau Peninsula then comes down the east side; make sure you know which leg you're on and which leg your destination is on.
The islands are accessible by private motorboat or by commercial ferry:
Manitou Island Transit
P.O. Box 1157, Leland, MI 49654 several miles north of the mainland part of the park, on the west leg of M-22 +1 231-256-9061. (http://www.leelanau.com/m...) From mid-June thru Labor Day, they offer daily transportation to South Manitou with a 4.5-hour layover at the island, also suitable for day-trippers and Su/M/W/F/Sa to North Manitou no layover, so it's for campers only, as well as sunset cruises and scuba expeditions. In early summer they operate on a less frequent schedule, and in the fall they run a single ship to both islands on Su/W/F. Closed from the end of deer-hunting season thru April. Reservations recommended. $29 round-trip to either island.