First of all, there are two different operators of boat trips in the area.
Jökulsárlón glacier lagoon runs the amphibious boats. During the summer May through September there are lots of departures, at least one every 30 minutes, last one leaving around 18:00 (6pm). The Jökulsárlón Café is open all year round. June, July and August it's open from 9:00 - 19:00 (9am-7pm) and the rest of the year from 10:00-17:00 (10am-5pm) excluding Christmas and New Years (23.december– 26.december and 31. December – 2. January).
Fjallsárlón is best known for being less known, a local favorite, and therefore usually more quiet. Fjallsárlón has a small local operator that runs 4 Zodiac boats that take up to 10 people per boat. This lagoon is really stunning and now a part of our Glacier Grand Slam trip. The boats on Fjallsárlón are operated from May through September and depart every hour. As they are quite full during the season, make sure you contact them and book beforehand. Glacier Grand Slam tour has a fixed departure each day with the Fjallsárlón team.