Although we ordinary Catholics cannot vote in the Conclave, we do have a duty to pray for the Cardinals during this time, and to beseech heaven for a good and holy man who will lead the Church. That's why I was so pleased to find Adopt A Cardinal. You send in your email address, and get given a random Cardinal to pray for.
You pray for him to make a good decision, not for him to become Pope (though that is a possibility, obviously!)
Wikipedia page about him, he is a member of the Congregation for the Causes of Saints. That means that he gets to investigate miracles. I like to think that looking at miracles would give one a firm appreciation of spiritual things and having prayers answered... it seems so very... well... Catholic! Helping the poor and working for justice and peace are important, but one doesn't actually have to have faith. Plenty of atheists would behave the same way, though without the benefit of grace.
Over 80,000 people have adopted a Cardinal, and its comforting to think that each of the 115 electors will have nearly 700 people praying for him during the run-up to the Conclave (and during it, naturally, as well as for three days after the election!) Do go over and adopt your very own Cardinal!