Two people can marry in Wyoming if they are:

Over 18 years old (or meet requirements for an exception)
Not already legally married to someone else or each other
Not closely related to each other
Legally competent to enter into a civil contract

Yes. It is now legal to marry a same-sex partner in Wyoming. Wyoming will also recognize same-sex unions legally performed outside Wyoming.

If a person is under 18 years of age but least 16 years of age, the county clerk must have the consent of the minor’s father, mother, guardian or person having the care and control of the minor, unless a Wyoming judge approves the marriage and authorizes the county clerk to issue a license.

If a minor is under the age of 16, the minor must obtain a court order before he or she can get married.

No. You don’t have to be a previous or current resident of Wyoming to get a valid marriage license.

To get married in Wyoming, you must both go to a County Clerk’s office in Wyoming. The couple must pay a fee to obtain the marriage license. In addition to the fee, the Clerk’s Office will want:

A copy of your driver’s license or other photo ID,
To know your social security number, your birth date, and birthplace (State),
Your parents’ full names including both mothers’ maiden names, and
The birthplaces (States) of both mothers and fathers.

If previously married, the date of divorce or date of spouse's death must be provided.

In Wyoming, a judge, magistrate or a licensed or ordained minister may perform the wedding ceremony.

No. Wyoming does not recognize “common law” marriages. The fact that you consider yourself married, or the fact that you have lived together for a certain number of years, does not mean that you will be considered “married” under Wyoming law. But, if the state where you came from recognizes common law marriage and your relationship qualifies there, then Wyoming law will recognize your common law marriage.

NOTE: There is no common law divorce in Wyoming, either, and even if you were common law married in a state that recognizes common law marriage, you have to follow all the divorce laws in Wyoming to obtain a divorce. Click here for more information on divorce in Wyoming.

A marriage can be annulled if either or both parties entered into the marriage without meeting the legal requirements to marry. An annulment may be granted when:

One or both of the parties is under the age of 16 when married without a judge’s consent;
One or both of the parties is under the age of 18 when married without parental consent;
The couple separated while one or both parties were under the age of 18 and the parties have not lived together while both were adults;
One or both parties were mentally incompetent at the time of marriage;
One party is physically incompetent and the action is brought within two years after the marriage.

If you decide to change your name after marriage, the first place to go is the social security office for a new social security card. You must bring your original marriage certificate and proof of your identification, like your driver’s license or passport. In addition, you must fill out a social security application. You can print this application and bring it with you or you can fill one out in the office.

Once you get your new social security card with your new name, then you may get your driver’s license and start changing your name on your other documents.

NOTE: Do not use your new name when making your travel arrangements for your honeymoon. Your name on your travel documents must match your identification. For instance, if you are flying to your honeymoon destination, then your driver’s license or passport must match the name on the ticket reservation. If you reserved your flight ticket in your new name and haven’t changed your name on your identification, you may not be able to get on your flight. It will take several months to receive new identifying information with your new name on it.

Prenuptial Agreements: Who Needs It and How Do I Make One? (What you need to know if you're considering a prenuptial, or premarital, agreement)

A prenuptial agreement ("prenup" for short) is a written contract created by two people before they are married. A prenup typically lists all of the property each person owns (as well as any debts) and specifies what each person's property rights will be after the marriage.

By Nolo.com

Your County Clerk's Office; or
Legal Aid of Wyoming at 1-877-432-9955