I've run six marathons and a bajillion shorter running races and triathlons, all starting with running 5ks in high school...so I come from a place of experience.
Get fitted for running shoes -- and by this I mean go to a running-specific store, not a Dick's Sporting Goods or similar. The fitters at a running store should watch you run or walk and tell you what shoes will work best for you. This can save you a lot of pain down the line.
Couch to 5k is always what I recommend to people. I believe they also have free podcasts for download.
My biggest advice is DO NOT worry about speed in the beginning. People tend to assign some arbitrary speed as being acceptable to them, and it quite simply doesn't matter. Your runs should generally be done at a pace where you could talk (not just gasping out one word

). If you feel like you're dying, slow down -- it seems logical but so many people assume they just can't run, when they're actually just running too fast for their fitness level.
Following a conservative plan like C25K and avoiding running too fast will help you gain endurance safely and avoid injury. Most people will find that they run faster on race day simply through adrenaline and excitement (for example, I ran 10 miles on Wednesday at around a 9:15/mile pace, but when I race a 10-miler, it's at around a 7:30/mile pace).
I live for this stuff, so let me know if you need more advice.