Great answer from Paul, which I'd like to add just a couple of things to. The purchase period is for a property that has a closing date on or after January 1, 2009 and November 30, 2009. (NOTE: properties closing on December 1 are not eligible for this tax credit!)
So if you've already bought and closed on a property, and you meet the other criteria (adjusted gross income with in the 75k/150k limit and 1st time buyer/non-property owner for the last 3 years) you can claim this credit on your 2008 taxes. If you are already filed your 2008 federal taxes, you could file an amended return to claim to the credit in 2008 or just wait until 2009.
If you HAVEN'T yet bought a property, here is an interesting twist. Prospective home buyers who believe they qualify for the tax credit are permitted to reduce their income tax withholding. Reducing tax withholding (up to the amount of the credit) will enable the buyer to accumulate cash by raising his/her take home pay. This money can then be applied to the downpayment.
Here is a great website that you may find helpful: http://www.federalhousingtaxcredit.com/2009/glance.php
I wish you all the best, and If I can help answer any questions on the buying process in our area, you are welcome to contact me at your convenience.