Since I started running just a few years ago, I have a lot of fresh advice for first-time runners.  Here are a couple of suggestions to get you started:   

The first thing you need is a good pair of shoes, so if you've never bought running shoes before, I would suggest going to a specialty store and having the shop assistant help you pick a pair.  Everyone's running step is a little different, and at a good store they'll have you try out the shoes on a treadmill to see if they work for you.  For example, I over-pronate (my feet roll inward when I run).  I learned that I need to buy so-called "stability" shoes, and they really helped my step.  After the first time, you'll know what kind of shoes you need, and you can shop around and look for good deals. 

Once you have proper shoes, you're ready to start running!  There are tons of plans for beginners out there, and you'll need to take your running goals and past athletic experiences into account when choosing one.  The best advice that I can give is to start slowly.  Running is quite hard on your knees and joints, so even if you are in very good shape, be careful not to start out too hard.  Many people prefer to begin with a run/walk program and work up to running for their entire workout.  Also, you should take at least 2 rest days per week (on average, I run 3-4 days per week and may take a yoga class one other day).

Finally, I highly recommend Dawn Dais' book, The Non-runner's Marathon Guide for Women.  It's funny, sarcastic, and full of good advice for first-time runners.