Expert makeup artists are always telling their clients to use an eyelash curler before applying mascara. However, I have never been able to see a difference. Can anyone tell me the proper way to use these things?

Try a higher end curler such as the Mini Eyelash Curler from Talika. It only takes seconds and works brilliantly. If they still don't curl perhaps it's just the lashes themselves, meaning they are just stick straight and simply will not curl. Try a curling mascara instead.