Have a friend grasp the back (lighter) end of the elliptical frame and lift it off the ground. The crossbars the back end of the elliptical frame rests on make great handlebars once it's up off the ground.
Hold onto the front of the elliptical frame to steady it. This is the heavy end of the elliptical, so unless you're moving it up or down the stairs, you should leave this end on the ground and simply push the machine. If you have to move it over delicate flooring, see the Tips section for important advice.
Steady the heavy end of the elliptical as you push it and your friend pulls on his end to move it. Try to move the trainer's back end first; because you're in control of the heavy end, you should be facing forward and able to see where you're going.
Go up and down stairs, if necessary, light end first. Recruit a third friend to help you carefully lift the heavy end down one step at a time as your friend at the back end of the machine carefully steadies it from below. If you need to rest, he can raise the light end of the machine to keep it more or less level while the heavy front end rests on the steps.
Adjust the elliptical trainer exactly as you want it in the new position while you still have your friends available to help.