One of the ways the Lord chooses to reveal Himself in the OT is through a mysterious character known only as the Angel of the Lord. The confusing thing about this Angel is that sometimes He is identified as a messenger for God and sometimes it seems as though the Angel is actually God. The very first time God uses the Angel of the Lord is not ironically to a patriarch, but instead to Abraham’s slave girl Hagar. In Genesis 16:7-10, the Angel of the Lord finds her and promises her He will give her offspring that can’t be numbered, a promise seemingly only God could make. The next time the Angel of the Lord speaks to her in Genesis 21:17, it is from heaven and names God as distinct from Himself (or speaks of Himself in the third person).
Perhaps the most confusing passage is the burning bush episode with Moses. In Exodus 3:2, the Angel of the Lord is said to be speaking in the bush, yet as the passage continues the “person” speaking is referred to as the Angel, the Lord and God almost as if they are interchangeable. You can see the Angel of the Lord with Moses again in Exodus 14:19 (here called the Angel of God) after the Red Sea crossing. However when Moses goes and speaks and sees the Lord on Mount Sinai, he is not said to speak with the Angel of the Lord.
Another place you will find a more belligerent Angel of the Lord is in Numbers 22:22. God is not too happy with Balaam and so the Angel of the Lord stands in his way, 
but Balaam doesn’t see Him although his donkey does. After the whole talking donkey thing, the Angel of the Lord opens Balaam’s eyes and speaks to him.
You can find two more big encounters with the Angel of the Lord in Judges. The first is to Gideon in Judges 6:11-23 where Gideon panics because he thinks he will die after seeing the Angel of the Lord face to face. However, Gideon does not recognize the Angel of the Lord at first, which might change the mental picture you have been building. The Angel of the Lord appears again to Samson’s parents in Judges 13:3-23 who identify him as a man of God at first, but then make a claim that they have seen God. Manoah, Samson’s father, asks the Angel for His name and He replies that it is wonderful. Good luck figuring out that one.
There are a few theories about the identity of the Angel of the Lord, one being that it is a pre-incarnate Christ. This is mainly based on the fact that the Angel of the Lord does not appear or speak after Christ comes, but there is no other good evidence that He truly is a pre-incarnate Christ. We do know that the Angel can appear or speak from heaven or in dreams. He can also perform the supernatural and while not always immediately recognizable, the sight of Him is overwhelming and leads most humans to label Him as the Lord. I think the most logical solution is that He is a messenger for the Lord like a modern day agent. He speaks for the Lord and appears in His stead probably due to the point God Himself makes in Exodus 33:20. Like an agent or ambassador for a county, where the messenger generally personifies the party represented, sometimes the Angel speaks as if He is the Lord. As for the humans reacting to Him as God, we can only assume that the sight of an angel is overwhelming enough to confuse even the most theologically sound.
References:
- Everlasting Dominion: A Theology of the Old Testament
- Genesis 16:7-10, Genesis 21:17
- Exodus 3:2, Exodus 14:19, Exodus 33:20
- Numbers 22:22-35
- Judges 6:11-23, Judges 13:3-23