In the past, it was very normal for parents to decide their child's marriage partner, and not the child him/herself.
"In the past"＝「過去には」
"it was very normal for parents"＝「親にはとても普通だった」
"to decide their child's marriage partner"＝「彼らの子供の結婚相手を決めることが」
"and not the child him/herself."＝「子供自身ではなくて」
☆「親戚」も含める文章ですと、"In the past, it was very normal for parents or relatives to...."と始めることができます。
アメリカ合衆国 
