Plan to dress lightly. Casual summer clothing--sandals, shorts and short sleeved shirts are suggested. Rain gear is always appropriate, but remember the high humidity; you may get just as wet wearing your raincoat as not! If you plan to hike in the park's interior, wear sturdy boots. Since the islands are volcanic in nature, lava rubble is found everywhere; it can be rough on lesser quality boots and shoes. Bring your own snorkel equipment, especially when visiting Ofu island.
Lastly, if you'd like to be closer to the local culture, you may wish to try a "lava lava", a skirt-like garment worn by both men and women in various styles and lengths. They are available at many local stores.
NOTE: It is customary in Samoa to cover much of the body. It is expected that men and women cover their shoulders and knees. Even when swimming, be sure to wear modest clothing; no bikinis, please.