Farmington has a small regional airport (FMN) served by American Eagle flights from Dallas/Fort Worth and Phoenix, with connections onward. Most visitors drive: from Albuquerque it's about three hours north on US-550 through the desert — a good road with interesting scenery. From Denver it's roughly four hours south via US-160 and US-550 through Durango.
From Durango, Colorado (45 minutes north), Farmington is an easy day-trip base for anyone exploring the Four Corners region from the Colorado side. A rental car is essentially mandatory — there is no useful public transport in this part of New Mexico, and the key sights (Chaco, Bisti, Aztec) all require your own vehicle.