Prepare for the worst case:
This situation reads like your manager is laying the groundwork to fire you. In your position, I would expect that in 30 days, you'll be called into your manager's office and will be fired. Yes, even if you improve, and no, there's probably nothing you can do at this point to change that. At the very least, your manager has already made up his mind that he wants to fire you, and will seize any excuse to do so.
And frankly, even if that's not the case (which I believe to be vanishingly unlikely), it's always good advice to prepare for the worst while hoping for the best, so the wise thing to do is prepare yourself for being fired in a month, regardless.
As such, the only option you have is to get a new job, before you lose this one. (It's often said that the best reference for a job is currently having one, so if you wait until after you're fired, you will find it substantially more difficult to get another position.)
Hope for the best:
However, while it's important to be prepared for the worst case scenario and look at other options, you'll still want to keep your boss happy and work on "improving" according to the plan he gave you. (The other answers here have covered how to go about doing that much better than I could, so refer to them for how to do that.) If nothing else, showing improvement and keeping the boss happy will at least give you a little room to breathe... and if you don't improve, you might find yourself fired sooner than 30 days from now, as noted in your PIP.
But again, because it's so important to prepare for being fired at the end of your PIP, outside the hours of 9-5, you should be pounding the pavement hard and procuring a new job (and over your lunch hours, too). Getting a job offer or two is also the only safe way to stick around and find out whether or not you're going to get fired, should you be hellbent on not switching jobs for whatever reason.
It sucks, and I've been there myself, but that's really what's best for you.