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Here is some info from the IRS (it's surprisingly straight forward).

Are you eligible? The majority of people who file a 2007 income tax return qualify, and many who don't regularly file a tax return may qualify as well. You're eligible if you have a valid Social Security number (SSN), can't be claimed as a dependent on a tax return and have either an income tax liability or "qualifying income" of at least $3,000. Qualifying income includes any combination of earned income and certain benefits from Social Security, Veterans Affairs or Railroad Retirement. Supplemental Security Income (SSI) does not count as qualifying income for the stimulus payment. Additional information is below, and a full legal description is available in Revenue Procedure 2008-21.

How much will you get? The actual amount depends on the information contained on your tax return. Eligible individuals will receive between $300 and $600. Those who are eligible and file a joint return will receive a total of between $600 and $1,200. Those with children will get an additional $300 for each qualifying child. To qualify, a child must be eligible under the Child Tax Credit and have a valid Social Security number. We have various examples for you check out.

The payments phase out at certain income levels, so those with higher incomes may receive a reduced payment or even no payment.