Darning is made easier if you have a darning-mushroom - it's helpful to have the cloth nicely stretched and firmly held. (Or you can tack the cloth to a piece of paper. Or use a doorknob. Or a lightbulb. Or a lemon! Or a wooden craft egg. Or a plastic easter egg, and you can keep the darning kit inside it.)
Other tips that a happy hour of meandering research has turned up - darn on the wrong side of the fabric; on knits, make the second lot of stitches on the diagonal, for more stretch; you can get thin reinforcing thread for darning heels of sox. And - do the darning when it's wearing thin, rather than when it's worn through!
Back in the good old days, before everything was throwaway, the important skill of darning was taught in school, and girls made darning-samplers. (Images from here and here.)