The role of the individual in his social environment changed as the Roman law developed through the ages. In the earliest era of Roman history the emphasis was not on the individual but on a clan (gens), to which he belonged. Gradually, the division between clans was replaced by the division on two communities: the Roman state as a community of citizens (populus Romanus Quiritum) and each of the individual families. Roman word familia does not have quite the same meaning as the modern term family. It is not defined by the family ties between members, but the father's or husband's authority (potestas or manus) over other family members. The word familia also denotes family property.

The original purpose of the family was for the most part economic. At the time when farming was basicly the only means to provide livelihood, familia constituted a fundamental economic unit. With the management of its own assets it was responsible for its existence. Communal assets and subordination to the father's authority were its fundamental characteristics.

The head of the family was pater familias, who had full power over people and property. He gained authority over the children when they were born or with adoption. Authority over wife was acquired with a special form of marriage which was essentially a legal transaction called mancipation.

Mancipation had been used for various purposes. It had been used for the transfer of ownership on property. In addition it was used for creation of testaments. And as already said it was an instrument to enter into marriage in which the wife came under her husband's authority. It was a »quasi« transfer of title. Wife was »bought« from her father (until marriage she was under her father's authority). Mancipation was a solemn transaction, which involved the transferee, transferor, five witnesses and a man who weighed the purchase price in copper on a scale. Definite words were prescribed to be said for the validity of the transaction. Prescribed form in which the mancipation had to take place had the effect of proof that the marriage really happened.

Source: Kranjc Janez: Rimsko pravo, GV Založba, Ljubljana 2010

While we know more about "elite" traditions and rituals than those in use among the lower classes, even for the rich there was no registry office, nor any official state role in marriage (or divorce) in the Roman Republic or Empire, at least until the official conversion to Christianity. (Adultery did have some presence in the criminal law, but mostly as it pertained to the rights of the cuckold.)

All this could lead to confusion, but usually there were witnesses of the ceremony and family members who could testify as to the marriage (don't discount the power of things being common knowledge); and nearly always it would be possible to refer to the tabulae nuptiales, which recorded the contents of the dowry paid, and any applicable agreement regarding restitution. As it was effectively a written contract for the transfer of goods, it would be carefully preserved. That is the closest thing to documentary evidence of the marriage in the modern sense.

Take a look at Karen Hersch's book, "The Roman Wedding: Ritual and Meaning in Antiquity" (2010).