See similar question and reference from Manu Smriti
Of the 8 types of marriage, the first and foremost is Brahma type, where groom's family comes searching for bride, and she is given as kanyadaan to a brahmachari who has completed gurukula and done samavartana.
It is to be done "Pradanam prak rtoh:" - Before Rtu (menses)
Marriage for girl is same as Upanayana for boy - they both have to surrender to someone at age 7 - 16 - boy surrenders to guru, girl surrenders to husband. 7 is lower limit (but not hard limit, it can be done earlier for spiritually advanced aspirants) , 16 is upper limit, according to shastras, for both upanayana & marriage. Beyond this, it loses both effectiveness and charm.
There are prayaschittas for late doing too, but don't know how many people do it, or how useful it is.
Source - http://kamakoti.org/hindudharma/part18/chap5.htm , and other chapters dealing with age of marriage, and why 'progressive' thinkers tried to increase age of marriage, and how Britishers passed law to enact Sarda act even though opinion among people was split 50-50.
Even on this site, 'forward' thinkers are going to post comments arguing against this saying it goes against 'Constitution', which was a document copied from constitutions of various countries, written within past 100 years, in mlechha basha, with little consideration for Bharatha Kalachaar and her ancient Dharma Shastras.
As I mentioned in a comment above, Child marriage does not mean child-physical relations.. the girl is only sent to husband's home after puberty.
You have to build a protective wall around the heart before lust enters it, that is the reason for doing upanayana and marriage before puberty. But nowadays most people don't follow this - boys get upanayana at age 24 and girls marry at age 24.
You can clearly see lustful consequences in society today of not following both above practices.