The best way to remove false eyelashes is by using a water-based eye makeup remover. It is important to be sure that the makeup remover you use does not have oil in it. Any oil can ruin the lashes so that you can't use them again.
To take off your lashes, simply soak a cotton ball or cotton pad in the water-based makeup remover, then close your eye and lay the cotton over the base of the lashes, making sure that the makeup remover is coming in contact with the area where the glue was applied. Leave it sitting there for about 30 seconds to dissolve the glue. 
When the time is up, simply remove the pad and the eyelashes should easily pull away from your lid. You can start taking them off by grasping one edge of the lashes and gently pulling toward the other side. If you encounter resistance or if it seems like the glue is still too sticky, you can reapply the soaked cotton ball to the base of the lashes for a little longer to finish dissolving the glue. Once the lashes are off, you can then use a cotton swab dipped in makeup remover or oil to get rid of any remaining adhesive on your eyelid. 
Alternatively, you can dip a cotton swab in water-based makeup remover and run it along the lash line to start dissolving the glue. Hold the tip of the cotton swab directly against the base of the lashes and start gently spinning it in your fingers, applying soft pressure against the lash strip. As you continue rolling the cotton swab, the lashes will loosen and come away from your lids. You shouldn't have to pull on them at all, meaning that this removal technique is extremely safe for the delicate skin around your eyes. This video provides an excellent demonstration of this technique: