How did Adam become Eve’s husband?  Was there some sort of ceremony to declare them husband and wife?

There is no doubt that Adam and Eve were married.  She is referred to as “his wife” immediately after God created her.  In fact, Moses was inspired to give the reader a command concerning marriage right after giving us the record of her creation (Gen. 2:21-25).  Jesus later quotes this same passage while talking about marriage and how it is supposed to be something which man does not separate (Matt. 19:3-6).

Yet there is no record in the Bible of any kind of wedding ceremony in the Garden of Eden to consecrate Adam and Eve’s marital union.  From a history standpoint, wedding ceremonies originated in the mind of man sometime after Eden.  We can read of a wedding ceremony Jesus attended in John 2.  However, we never read in the Bible that wedding ceremonies were commanded by God as something that is required in order to make a marriage legitimate.

The only guidance the Bible gives regarding what is necessary to start a marriage is that the laws of the governing authorities must be obeyed (Rom. 13:1-7) as long as they do not violate Scripture (Acts 5:29).  Those laws are different depending on the nation or culture in which one lives.  In America today, one is not legally married unless one has a marriage license.  Therefore, God would require a couple to obtain a marriage license in order to get married.  Anything else such as a wedding ceremony is optional.  I would advise engaged couples to remember as they plan the start of their marriage that a wedding is only one day, whereas a marriage is a lifetime.  Don’t make the mistake of putting all your focus on making that one day special so that you are not prepared to make every day afterwards special as a married couple.