I love how the Catholic Church encourages us to embrace the love of Christ for each particular person. We spiritually adopt unborn babies, priests, and now cardinals for the upcoming papal conclave. First, go to the Adopt a Cardinal website. When you have been given a particular cardinal's name, pray in a particular way for him during the conclave -- for his openness to the Holy Spirit, for his guidance, for his perseverance in serving the Church ... really for whatever you feel called to intercede for him.
Perhaps your cardinal will become the next pope, or perhaps he will lend his voice to communicating what the Holy Spirit asks of him. We won't know exactly what each cardinal says or does during the conclave, but we can rest assured that our prayers for each of them are a way for us to serve them, as they serve us.