As explained in "Permanent (Immigrant) Visa > Family-based", you can obtain permanent residence (green card) based on your marriage, if your U.S. citizen or permanent resident spouse files an I-130 petition, and once the petition is approved and your priority date becomes current, you apply for an immigrant visa at a U.S. Embassy/Consulate abroad (or apply for adjustment of status if you are already in the U.S.). You can also come to the U.S. as a K-1 fiance(e), marry within 90 days, and apply for adjustment of status in the U.S.
Conditional Permanent Resident Status
1. If your marriage is less than 2 years old at the time you obtain permanent residence (green card), you will initially receive a 2-year "conditional" permanent resident status, because the immigration law presumes that any marriage that is less than 2 years old was entered into solely for the purposes of obtaining immigration benefits. In order to remove this condition and become a permanent resident without condition, you and your spouse must jointly file a Form I-751, Petition to Remove Conditions on Residence, along with supporting documents to prove that you and your spouse have maintained a bona-fide good-faith marriage, during the 90-day period immediately before the expiration of your 2-year green card.
2. If your child received conditional resident status within 90 days after you did, then the child can be included in your I-751 petition. However, if your child received conditional resident status more than 90 days after you did, the child must file a separate I-751 petition.
3. Even if the marriage has become not viable but has not been terminated (in other words, if you and your spouse have been separated or no longer share a household as spouses but have not divorced), the I-751 petition may be approved as long as you submit sufficient evidence showing that the marriage was entered into in good faith and with a genuine desire for a marital relationship and not solely for immigration purposes.
4. If you fail to timely file the I-751 petition jointly with your spouse, or if the I-751 petition is denied, USCIS may initiate removal proceedings against you.
5. If you have been battered or abused by your U.S. citizen or permanent resident spouse, you can file the I-751 petition on your own, at any time after you became a conditional resident but before you are removed from the U.S.
6. If you and your spouse are divorced, you can file the I-751 petition on your own, at any time after you became a conditional resident but before you are removed from the U.S.