On Sundays and bank holiday Mondays from late May to September, a number of minibus services aimed at hikers shuttle around various locations within the national park; all are detailed on the Moorsbus (www.moorsbus.org) website.
For example, the Moors Explorer service runs from Hull to the Moors National Park Centre in Danby with stops along the way, but only runs six or so times a year. An all-day hop-on, hop-off ticket costs £12.50. Download the EYMS app with timetables and track bus arrival times live.
The North Yorkshire Moors Railway, running between Pickering and Whitby, is an excellent way of exploring the central moors in summer.
If you're planning to drive on the minor roads over the moors, beware of wandering sheep and lambs – hundreds are killed by careless drivers every year.