You're kidding me. You want to be a pundit? I mean, if it's your cup of tea, sure. But it's a brutal game. It's less substance, more performance, and the ability to hijack conversations. Barney Frank is a fucking master at this; if you've ever seen him on a talking show, you can see how he hijacks the conversation (whatever it may be) to talk about his latest book. He has page numbers memorized. You alternate between wanting him to shut up to admiring the sheer skill.
In any case, here's the basic route for an analyst:
1. Get into a good school. Top 20 or so, preferably Ivy or as good, with plenty of opportunity for connections. Relevant majors are political science, foreign affairs, history, journalism, international relations, etc. For you, consider philosophy (teaches you logic and logical thinking, "because of x there is y", which really helpful in law and/or arguing/debating).
2. Hone investigation and analysis skills. Much of the job includes researching and analyzing data. So developing data interpretation and investigative skills is really beneficial. When you're in my position (ie, pouring over white papers/corporate research reports/books, underlining anything of substance, taking notes, etc) you'll find that being half-way decent at this is a godsend. Take classes that encourage this (seminar classes where the professor can review your work individually is good for feedback). While on the subject: take public speaking. It's a critical skill, more so for your aims.
3. Extracurricular. Join the relevant clubs or groups on campus. You want like-minded peers (or what passes for them) that you can network with and chances to improve yourself. Debate society, Newspaper, College Republicans/Democrats/Libertarians/whatever, etc. Feel free to consider starting your own organization/group if nothing interests you; it's harder work, but makes for good resume material, particular if you can make it last. Freebie idea that I never got to implement: a Republican/conservative version of Roosevelt Institute Campus Network. Think about it.
4. Internship(s), since they introduce students to how politics affect different industry sectors and the political process. Get one, ideally a solid one. Key places are in government agencies, a Congressman's staff, or think tanks. For you, also consider media companies, along with the Government Accountability Institute, which I mentioned before.
5. Find a relevant post-graduation job. If you did well in the internship(s), you may already have offers.
Final bit of free advice: read.
There is the daily news, for which I suggest RealClearPolitics/World, Politico's Playbook newsletter (particularly on weekends, when they give a list of informative longreads), and Foreign Policy's Situation Report newsletter (somehow relatively untainted by Rothkopf. He's ruined Foreign Policy, killing substance and focusing on sensationalism).
But ideally, you want to devour books on a wide variety of subjects. Ideally, you want the good academic stuff, not the pablum written by existing pundits. Analysts are at their best when they develop a holistic approach to viewing things and just know a lot in general.