Prudence is the grace to form correct judgments (Mt 10:16; 1 Pt 4:7). It is "right reason in action". (ST II-II, 47, 2) It is what "disposes the practical reason to discern, in every circumstance, our true good and to choose the right means for achieving it." 
Being prudent, then, involves two steps: (1) knowing what is right, and (2) doing it.
Prudence is a primarily intellectual virtue; it's about using your head, as Fr. Hardon once simply put it. It guides the other human virtues of fortitude, temperance, and justice by telling us when and how to apply those virtues. The more we are catechized, the more we renew our minds with Scripture, the deeper we delve into the sacramental life - all the more our minds are fit to know God's will. The simple answer to improving this intellectual virtue is to use your mind - work it out in Scripture study, catechism reading, and prayer.
However, that knowledge cannot simply stay in the head. Knowing what is right is useless without doing what is right. This is hard part, because "the spirit is willing but the flesh is weak". (Matt 26:41) We must pray constantly not only to develop prudence but to will what God wills. Our fallen natures - weak flesh - makes it very difficult to put that knowledge into action, but the more we try, the more success we have. Today, I may only have had moments of success, but God will build on those moments. Pray for prudence and grace to do God's will, and also be patient as the living water flows through those tiny cracks and slowly opens them up!
Aquinas, St. Thomas. Summa theologiae.
Hardon, Fr. John A. The Virtues. Available from http://www.therealpresence.org/archives/Virtues/Virtues_001.htm. Internet; accessed 25 June 2010.