i'd defintively use tire irons, spoons or similar, or a tire machine. it also depends on the tire you're using. German Heidenau tires for example are very heavy, no chance wrestling those over the rim without some leverage...
i'd also seize the opportunity to check the wheel balance while you have the old tire off. or at least have the wheel with the new tire balanced. Or use balancing beads.
i always slip the wheel on one bead of the tire (check the rotation) then slip in the lightly inflated tube. Fhenagle the valve stem through its hole (make sure the stem retaining nut is on the off), rotate the tube/tire so that the valve stem sticks out at a right angle, then start mounting the second tire bead. inflate to light pressure, then check if the beads have seated all around. if the tire has a low spot, bounce the wheel off the ground, re-check, then inflate to pressure. check the valve stem angle, if its still perpendicular to the rim, put on the small retaining nut over the stem.