If a person marries a U.S. Citizen for the sole purpose of obtaining permanent residence (Green Card), that person is committing the crime of immigration fraud. This person can be deported and forever barred from re-entering the U.S. The Department of Homeland Security actively investigates suspected cases of marriage fraud through various means including:
Requiring a great deal of evidence to prove the bona fide nature of the marriage including phone records, emails, IM communications, photographs, affidavits, receipts, checking account information, and tax records.
Interviewing the husband and wife separately.
If, on the other hand, you happen to fall in love and marry an American Citizen, you may apply for an adjustment of status to lawful permanent resident (Green Card holder). But, this is not an easy process and it requires a lot of good documentation. Even if you are granted the adjustment, you will most likely return for another interview two years after the original Green Card is granted. At the end of the two years, you may also be asked to provide further documentation of the valid nature of your marriage for the past two years.
It might be possible. If you entered into a valid marriage with a US citizen you may be able to obtain lawful permanent resident status (it will be conditional) if you apply based on marriage that is less than two years old. But, just marryng a US citizen itself does not mean you are eligible. There is a lot more to it.
A major issue is first to make sure if you are even eligible and second if you are eligible, whether you can apply in the US or if you have to return to your home country to process your application (which could cause certain bars from returning). These are complex issues and will depend in your immigration history (and criminal history if any). You should consult with an exprienced immigration attorney to determine if you are eliigble and to determine if you can process here in the US or not.