Hi, there are the 7 cannonical hours in the Agpeya: Prime, Terse, Sext, None, Vespers, Compline, and Midnight.
There's also the Vespers service, or the raising of the evening incense. It's confusing because this has the same name as one of the Agpeya hours, but vespers is just the evening paryer, so in the context of the Agpeya it's one of the hours, and in the context of the Liturgy it's the evening incense... I'm not sure how clear that was, sorry.
When you go to church on a typical Sunday (starting with the eve of Sunday) the first thing you should see is the prayer of the 9th hour of the Agpeya, the 11th hour (vespers) and the 12th hour. If you're not seeing this and the first thing you see is the Vespers praise it's probably being done quickly by a deacon inside to "get it out of the way" so the evening service isn't too long.
After these hours are prayed the Vespers Praise is sung.
After the vesperse praise comes the raising of evening incense, or Vespers.
Next comes the prayer of the Midnight hour of the Agpeya.
Finally the Midnight Praise.
In most Churches all these are done as one long service, but if you went to a monastary you'd leave at the end of vespers and come back later for Midnight Praise, it's not all one service, it's just all done at once because that's the only feasible way to do it when people have to travel to Church.
In the morning, first Prime is prayed from the Agpeya, and then the Morning Praise or the Doxology of Prime is sung. This is skipped in many churches.
After this comes the Raising of the Morning Incense, the the prayer of the 3rd and 6th hr of the Agpeya, and then the Liturgy of the Word and the Liturgy of the Eucharist.
So basically the three parts of the Liturgy are the Raising of the Evening Incesne, the Raising of the Morning Incense, and the Liturgy. Around these parts of the Liturgy, whatever hours of the Agpeya that relate to that part of the day are prayed. And then there are also the three Priase services. All three of these: the Liturgy, the Agpeya, and the Praise services together really make up the complete Liturgy for that day.
There are some variations: on days of fasting (which is never a Sunday) the Liturgy is later in the day, so the 3rd, 6th and 9th hours are prayed. If there's vespers that night, you'd start with the 11th hr since the 9th is already done. During the Great Lent, the Liturgy is even later in the day, so the 3rd, 6th, 9th, 11th, and 12th hours are prayed, and there are none left, so there is no Vespers for weekdays of Lent.
I don't know if that answered your question or not...