Nothing spoils an elliptical trainer workout like a persistent, annoying squeak coming from some undetermined part of the machine. Eliminate the squeak by making sure the machine is level, tightening any loose linkages, applying grease to the rollers and cleaning out the roller tracks.
Leveling and Loose Linkages
Ask a friend to stand behind the machine as you pedal, then move to the front and look from there. If she sees the machine rocking back and forth at all, adjust the levelers on each corner of the machine to eliminate the rocking; this might also eliminate the squeak. A single loose connection in any of the moving parts can also cause squeaking; use your ears to try to pin down the general area the squeak is coming from. Work backwards from there to properly tighten any loose linkages.
Rollers and Roller Tracks
If your elliptical trainer has rollers that glide in roller tracks, clean any dirt and debris out of the tracks with a clean, damp cloth. Avoiding using acid cleaners, which may damage the tracks or rollers themselves. The rollers and tracks should be greased periodically; once you've cleaned out the tracks, apply a layer of elliptical grease all the way around both rollers, then work the pedals until the tracks are covered in a thin layer of grease. If the squeaking still persists, clean any debris out of the grooves in the foot pedals with a soft scrub brush and vacuum.