Blanding is in one of the more remote corners of the continental United States. The nearest commercial airport is in Moab (about 90 miles north on US-191), which has limited service. Most visitors drive, typically from Salt Lake City (about 5 hours), Moab (about 1.5 hours), or Monument Valley (about 45 minutes south).
US-191 is the main route through Blanding, running north to Moab and south to Mexican Hat and Monument Valley. US-95 runs west through Cedar Mesa toward Capitol Reef. There is no public transport to or within Blanding. A car is not just helpful but essential — the sites you came to see are scattered across a large and roadless landscape.
Fill up on fuel in Blanding before heading into Cedar Mesa or Grand Gulch. The next gas station to the west is a long way away.