Marriages by non-citizens are legally binding unions. Aside from providing Social Security numbers, the requirements to get married in the U.S. are the same for both U.S. citizens and non-U.S. citizens. Passports are usually accepted as identification, but some locales may ask for certified copies of your birth certificates.
Before making any wedding or travel plans, you first check with the local county clerk or marriage official where you want to get married to make sure you have all the documentation that is necessary so that your marriage will also be recognized in your own home country.
It is important to recognize that states in the U.S. have different laws and requirements regarding marriage. These differences include age, blood tests, waiting periods, same-sex marriage, cousin marriage, etc.
What you want in your hands before you leave the country is a legal document to prove that your marriage is legal and recorded. That is what the marriage certificate is for.
If your home country is a member of the Hague Convention, it has agreed to recognize the public documents of other member countries when the papers are attached to an apostille. Some countries will require you to sign an official paper once you are back home.
Before Getting Married in the U.S.
1. Getting married in the U.S. does not change your immigration status, citizenship, or provide you with a Green Card, change your travel documents, etc.
"The intention of a travel visa is a temporary visit. If you want to get married during your visit then return home before your visa expires that's okay, but a travel visa should not be used with the intention of entering the United States to marry, stay permanently and adjust status. The fiancé and spouse visas are designed for this purpose."
Source: Jennifer McFadyen. "Getting Married on a Travel Visa." thespruce.com
2. Documents should be translated into English.
3. Double check to make sure your home country will recognize your marriage if you are married in the U.S. If you are already in America, you can ask your country's consulate in the U.S.
4. Under the public policy exception, if your U.S. marriage violates the public policy of your home country, then your marriage would not automatically be valid.
5. If you are having a destination wedding in the U.S. and intend on having family and friends with you, you need to make sure they have the necessary travel documents, like passports, too.
"In the past, marrying away from home usually meant eloping. The couple would steal away in the night to flee family disapproval or expectations and tie the knot on their own terms. Today, the idea has shed its stigma and a growing number of couples are hightailing it away from the traditional formal affair to a casual, intimate occasion in their dream honeymoon spot."
Source: "Destination Wedding Basics: Why Marry Away in a Destination Wedding?" TheKnot.com.