Changing from apples to oranges? No problem!

How do people break into finance (hedge funds, i-banking) when their concentrations in college had absolutely nothing to do with finance? I have been meeting (and reading about) people who have jobs in the financial industry, yet their backgrounds and majors (poli sci, history, etc.) have never entailed related experience that you would normally think is sought after in finance. I graduated with a degree in journalism and have always found an interest in the banking/finance industry - I'm currently a legal assistant for a law firm whose clients are major banks - but if there is a way to finagle my way into finance, I'd like to know how!