According to Tolkien in Morgoth's Ring's "Laws and customs of the Eldar" Elves were much like pre-fallen man. As a philologist Tolkien was trying to reconstruct a lost mythology for the Elves. Here's what he says about their families. Read the essay in Morgoth's ring for more depth.
They grow slower than mortals though their minds are faster, learning speech before the first year. Their wills master their bodies quickly so they learn to walk, dance, etc by their first year. Elf Children at play would resemble fair happy children of men with little need for governing. Their words, and mastery of their bodies would make them seem older than they appeared in body. Might appear to be seven when actually in their 20’s, having adult size 50 and full maturity at 100.
Elves in ancient times married once, early in life, for love and by free choice. They had few children, who were very dear to them.
Pregnancy usually lasted a year, and occurred early in the life of the parents. Eldar don’t deteriorate with age, but their bodies change as they age with long intervals between the marriage and birth of the first and subsequent Children. Their families were bonded deeply by love and kinship in mind and body.
The union of love is a great delight and the days of the children remain in their memory as the merriest in life.
Children needed little governing.
Seven children was the usual upper limit in ancient times, but in future ages, partly due to varying levels of corruption in various elven societies, these norms were often exceeded rarely, even when corrupted do they ever succumb to deeds of Lust.
They betroth each other early in life, subject to parental approval unless at a fitting age and intending to marry soon, at which point the betrothal was announced at a meeting of the two houses. They exchanged rings and the betrothal lasted at least a year, revokable by return of the rings. After betrothal, the betrothed appoint a time for the wedding when at least a year passed.
Seldom is betrothal revoked since they seldom err in such a choice, nor are they easily deceived as they are not easily swayed by bodily desires, being continent and steadfast. Marriage was celebrated at a feast of the two houses at the end of which the mother of the bride and father of the groom placed their hands together and said a solemn blessing, mother invoking Varda, and father Manwe as witnesses. No Mortal on antediluvian Earth has ever heard it, and the name Eru, seldom spoken in ancient times was used as well. They give back their betrothal rings and receive others worn on their index fingers. The bride’s mother gave the groom a jewel on a chain or collar.
While it was generally considered most appropriate to marry with family blessing and witnesses, consummation alone was the necessary and sufficient condition of a valid marriage. Such simple marriages were most common in times of exile or flight when ceremonies were impractical, but even in times of relative peace, "it was the act of bodily union that achieved marriage" (Laws and Customs of the Eldar).
Husbands and wives don’t always live together, and yet a sundering during the bearing of a child or its early years is so grievous to them that they prefer to have children in good times. It is possibly for this reason why the house of Finwë (and likely the other exiled Ñoldor) had such a low birth rate during their exile in the First Age (in contrast to beforehand in Valinor), due to the constant threat of danger, if not outright war and strife.