Marriage in ancient Hellas was a family affair. The father of the son--who was often in his thirties by the time he got married--opened negotiations with the family of a bride in her teens. The two families came to an agreement about dowry, a contract was signed by the father of the groom and the father of the bride in front of witnesses, and the groom met his new wife--often for the first time--before taking her to bed.
Men married to have children, and to have someone to tend to the home while he was out, dealing with public affairs. Romance didn't counter into it. Demosthenes, a prominent statesman and orator in ancient Hellas, once said: "We have prostitutes for our pleasure, concubines for our health, and wives to bear us lawful offspring."
These lawful offspring were so important that, if a wife had not bore a husband children by the end of the tenth year of their marriage, the man was forced to file for divorce. This was a costly affair because a divorce meant parting with the dowry that was paid to the husband upon marriage, as the ex-wife was entitled to it.
Should a husband die before producing offspring, the widow was encouraged--even forced--to take a new husband as soon as possible and produce a child with him. This first born child was considered to be the child of the widow's first husband and counted towards his family line and heritage. The practice was called 'raising up seed' and was a lawful and legitimate way of parentage, usually exectuted with the brother of the deceased husband. The custom of raising up seed also opened the way for the practice of adoption to sustain the family line.
Something that's important to understand is that children in ancient Hellas were born with a different sentiment than children are born these days. Children, now, are born out of love and a need of the parents to create something of 'theirs'. A child is precious, irreplaceable. We tend to have few children and place all our eggs in their basket(s). In ancient Hellas, families tended to be as large as possible. Children could help out around the house, the farm or with sustaining the family any other way but they also tended to die. Children were made for the hearth, not the other way around.
Giving birth was an incredibly risky ordeal in ancient times, for both mother and child. Stillbirths happened frequently and labor took mother and/or child quite often. Many children died in their infancy due to illness or malnourishment and should the children make it to adulthood, they had a good chance of dying in the Hellenic army. Many Gods, Goddesses and Nymphs were petitioned for aid in childbirth and the period directly after; Artemis, Eileithyia (Ilithya) and Phainō come to mind right away, but Hera, Adamanthea, Kynosoura and Maia were also responsible for childbirth and midwifery.
When a child was born, it was presented to the father, who had the right to refuse it as his own. In Sparta, the child was also presented to the Elders, who could refuse it, even if the father did not. If the child was refused--usually due to deformities which would prevent the child from performing his or her duties to the hearth--the child was left out in the woods as an offering to the Gods.
If the child was accepted, there was a celebration on the fifth or seventh day after birth called the Amphidromia (τὰ Ἀμφιδρόμια). The child was presented at the shrine to Zeus and Hestia by the father. This was observed by the family and gifts were given. If the child made it to the tenth day of life, there was another celebration, new gifts, and the child was named. Especially this last celebration was recorded as being postponed quite regularly. I suspect this was done to give the mother, who was to be present at this celebration, the time to stop bleeding from the birth. Once this stopped and both mother and child were cleansed of miasma, the ceremony could take place.
It almost seems logical to abstain from sex to avoid all of this but that did not happen; because if it did, who would tend to you when you grew old? Who would close your eyes in death and give you ritual burial? Who would give away your daughters in marriage? Who would cherish the memory of the dead and keep alive the institutions that were so dear to him? Who would, as was called, 'save the hearth' if there were no surviving children?
For the Hellens, honor was incredibly important. To receive honor was to be talked about after death; you would receive libations, gifts and continued family honor if you were remembered. It was up to your children--mostly the son's--to pour the bulk of these libations and to spread the word of your deeds and accumulated honor. Being forgotten by the living was incredibly frightful. As a result, the Hellens did everything they could to procure children who could continue the family line; celibacy was forbidden, law upon law was accepted to ward off childlessness... and the hearth survived.