National Public Radio tends to do a great job of following most significant modern issues. Their drivetime news programs are pretty cut-and-dry, while their entertainment programs (usually on the weekends) lean quite liberal. They also do a terrific job of providing variety with music and movie reviews, interviews with INTERESTING celebrities and politicians, science, and finances. Just be warned - because there is such variety, they sometimes get some really boring material too.
If you want to figure out what is actually going on with the economy beyond the DOW going up or down, or "it's bad", the Planet Money podcast is arguably the best thing on the planet for explaining complicated financial situations in relatively plain language, gradually giving you a really good view of the big picture. Radio Lab podcasts are also really interesting science shows similarly done in a manner that makes complicated concepts easy to understand. Both are available for free through iTunes.
If you're in college, take a couple political science or western civilization classes to get a good idea of what is going on and why. Modern history (World War II to current) can really help understand why a lot of things in the world are the way they are, and how they got that way.
Also, just think about stuff with an open approach. Realize that it's all people, and that every group will have its moderates and its radicals. Don't become so entrenched in your own worldviews that you can't possibly understand the thought process of those that disagree with you. Mostly, no one wants to talk politics with someone that only wants to talk and never wants to listen.
