Engagements were optional, but when entered into were contractually binding and financial consequences might follow if the contract were broken. An engagement party might be given by the bride's family, at which sponsalia, formal betrothal, could be announced. An iron ring (anulus pronobis) might be given by the man to his fiancee along with some money to help cover her wedding expenses. The bride brought her dowry with her, at least symbolically, to the eventual marriage ceremony.
Marrying persons would enter into ancillary contracts to assure that heritage and inheritance were preserved, but, if you were a Pleb, as most citizens were, or a freedman, you most likely wouldn't really have much of either to worry about. Slaves, a large percentage of the total population (at times more than half) bred or were bred and didn't have conubium, but they could be granted contuberium by their masters. Freedmen could take slaves in concubinitas if the master of the slave and former master of the freedman agreed.
Higher up on the social ladder, in rich cavalier and senatorial families, things got more complex. Marriages were often arranged to cement alliances or to preposition the male partner or the female's relatives for political or economic advancement, or to produce verifiable descendants either for dynastic reasons or simply to tend to ancestral spirits. In these cases, more public, legally binding, and sometimes religiously sanctioned contractual arrangements were made.
There were several types of marriage, and the differences had a great deal to do with property. There were no community property laws, and everything, even children, belonged to the father. The bride was also, legally, property, and to whom she belonged depended on the kind of marriage. If the marriage was "in manum", she and all of her property became the property of the husband (actually of his pater familias) and she was the equivalent of a daughter in her husband's household. If the marriage was "sine manu", the most popular kind of marriage by the first century AD, she and her property remained under control of her father's family.
There were three types of the more formal in manum marriage. Confarreatio was a complex and elaborate religious ceremony with at least ten witnesses and presided over by the pontifex maximus. Only children of parents married confarreatio were eligible, so, in practice, it was only used by a few very high ranking families. A ceremoneal bread (panis farreus) was used and gave its name to the ceremony. Confarreatio marriages were virtually indissolvable, and that fact was said to have led to occasional upper class murders.
In coemptio, the wife carried a dowry into the marriage but was ceremoniously bought by her husband in front of at least five witnesses. She and her possessions then belonged to her husband.
The third in manum marriage was the usus. After a year's cohabitation, the woman belonged to her husband in manum. She could end the marriage by staying away for three consecutive nights (trinoctium abesse) before the year was up. The process could be renewed annually and this preserved the options of the woman. If she opted out, she did not have to return to her birth family. This was sometimes used to get a girl out from under the domination of an abusive father without tying her permanently to a husband. A cooperative male would marry her in an usus marriage, from which she would then absent herself for three days. Since she was released from her pater familias, and since she wasn't in the hand (in manum) of her husband, she acquired some freedom but she also would lose the protection and support that family life provided. (This process was similar to selling a son into slavery to a friend who would immediately manumit him. But a girl, of course, did not thereby gain the right to start a family on her own.)
Marriage laws and rights gradually became extremely complex and legal precedent also gradually accumulated, but, for the most part, the complexities and precedents had a liberalizing effect and protected the rights (or at least lessened the disadvantages) of the female partner. Throughout the ancient Roman period, however, the purpose of matrimony was summed up in the word itself: matrimonium (with its root mater = mother) had as its main objective of the creation of children for the husband's family and for the state.
The Internet has Roman matrimony pretty well covered including a great deal of information on marriage law. For general information on marriage and matrimony, see the About.com links at: http://ancienthistory.about.com/homework/ancienthistory/cs/marriage/index.htm and the Roman Weddings page at http://ablemedia.com/ctcweb/consortium/ancientweddings5.html.
More detailed explanations of Roman laws concerning the subject, if you really must know everything, are at http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman/Texts/secondary/SMIGRA*/Law/home*.html#marriage