I think the reasoning evening Masses weren't as common prior to the 60's was that the communion fast was from midnight of the preceding day until the time Holy Communion was received.
The structure of Evening prayer is as follows:
Introductory verse ("God come to my assistance, Lord make haste to help me. Glory to the Father and to the Son and to the Holy Spirit. As it was in the beginning, is now, and will be forever. Amen. Alleluia")
Then a hymn may be sung or said
The first antiphon is recited then a psalm, then the Glory be, then the Psalm prayer, and then the antiphon is repeated.
The second antiphon is recited, then a psalm, then the Glory be, then the Psalm prayer, and then the antiphon is repeated.
The Third antiphon is recited, then a Canticle (from the NT at evening prayer), then the Glory be, and the antiphon is repeated.
Then there is a short reading, which in a communal celebration may include a homily.
Then the Gospel canticle is recited (with its antiphon and followed by the Glory be). At evening prayer it's the Magnificat, at Morning Prayer, the Benedictus, and at Night Prayer, the Nunc Dimmitus.
After the Gospel Canticle various intercessions/petitions are asked
The Our Father and the closing prayer are recited
Morning and evening prayer may end with a blessing by a priest or deacon if celebrated communally otherwise it ends with the verse, "May the Lord bless us, protect us from all evil, and bring us to everlasting life. Amen."