Everyone's case is different. Some will qualify, some will not. Only a lawyer can tell you whether you qualify.
You have to qualify before you can file an application under the new law.
If you qualify, you can file even if you have an order of deportation.
You have to have entered the US before you turned 16
You cannot be more than 30 years old now
You cannot have any serious misdemeanors or felonies
You have to have more than 5 years of residence in the US
You have to either be in school, graduated high school, have a GED, or have served in the military
If you qualify, you can get a work permit, a social security number, a driver's license, and other benefits.
WHAT IT IS, AND WHAT IT ISN'T
This is not "backdoor amnesty" in contrast to the vitriolic complaints of those like Gov. Jan Brewer of Arizona (who signed the rather infamous SB1070 "papers, please" law, prompting a legal challenge currently being decided by the US Supreme Court.) Amnesty means the granting of legal status to those who broke the law. No status is being granted to these hardworking people; it is simply a sensible, administrative allocation of resources that results in a more humane, just immigration system, and a net positive to the economy to boot.
Nor is it the "DREAM" Act, although few would argue that it's not a significant step towards the passage of the DREAM Act. Many of the young people that would have qualified for actual status had the DREAM Act passed are now likely to benefit from this new policy. But it's not circumventing Congress.
It's called prosecutorial discretion, and it's used by prosecutors in every courtroom in every day.