If she entered without a visa and/or was not inspected by an immigration officer, then she will not be able to become a resident inside the U.S.
She could get married to a U.S. Citizen (you) and then she could file an I-130 here in the U.S. (which will give her no legal status), but once that I-130 is approved, really the only thing she can do is leave the U.S. and apply to come back in at the U.S. Embassy/consulate in her home country as the spouse of a U.S. Citizen. At that point, they will want to deny her because she entered illegally and stayed. So she would have to apply for an I-601 waiver (forgiveness) and to get this waiver she will have to prove that her spouse will suffer extreme hardship if she is not allowed back in to the U.S. These waivers are very difficult to get. The reason they are difficult to get is because the hardship probably will need to be more than just economic hardship or emotional separation hardship. So because they are difficult to get, no one wants to risk leaving the U.S. and getting stuck outside for 10 years if it isn't granted.
You can look at this link to get more information on I-601 waivers. It is from the U.S. Embassy in Syria, but it is a good description and the process should be similar in all U.S. Embassies.
The only other "pardon" or "forgiveness" would be 245(I) which would only help if she has an I-130, I-140, or Labor Certification filed for her before April 30, 2001. If she didn't, then you have to go by what I said above. And as to how much it would cost...well, that could be anywhere from $2000 to as much as $10,000 or more. It is a good deal of money for not really a good chance of being granted, but the chances are better with an attorney involved.
This is VERY risky. You are gambling that they don't already know or don't have a way to find out. They might. They might do a background check to see her activities in her country over the last few years (I doubt that they would). But it is still a risk.
You'd also have her lying about being here, etc. So she might get away with it at the outset and even get a green card and even citizenship, but if they ever found out about it, even years later, she could lose the citizenship and the green card because they were procured through fraud.
DISCLAIMER: Answers from Experts on JustAnswer are not substitutes for the advice of an attorney. JustAnswer is a public forum and questions and responses are not private or confidential or protected by the attorney-client privilege. The Expert above is not your attorney, and the response above is not legal advice. You should not read this response to propose specific action or address specific circumstances, but only to give you a sense of general principles of law that might affect the situation you describe. Application of these general principles to particular circumstances must be done by a lawyer who has spoken with you in confidence, learned all relevant information, and explored various options. Before acting on these general principles, you should hire a lawyer licensed to practice law in the jurisdiction to which your question pertains.
The responses above are from individual Experts, not JustAnswer. The site and services are provided “as is”. To view the verified credential of an Expert, click on the “Verified” symbol in the Expert’s profile. This site is not for emergency questions which should be directed immediately by telephone or in-person to qualified professionals. Please carefully read the Terms of Service (last updated February 8, 2012).