The LORD [yehôvâh] said unto my Lord ['âdôn], Sit thou at my right hand, until I [yehôvâh] make thine ['âdôn] enemies thy footstool. (Psa 110:5)

yehôvâh : self Existent or eternal; Jehovah, Jewish national name of God: – Jehovah
‘âdôn : lord, master, owner (Referring to Jesus — see Mat 22:42-45)

In the Old Testament: Look Closely at how this is worded. In the Psalms David called Jesus Lord ['âdôn]. Jehovah is the name of the eternal God. We know that the prophecy was referring to Jesus because of how both Jesus and Paul referred to the verse in the New Testament.

Here in the Old Testament Jesus is already being referred to.

Another interesting thing is that Jehovah says to Jesus, “…until I [Jehovah] make thine [Jesus's] enemies thy [Jesus's] footstool.” Here in the Old Testament Jehovah is speaking to Jesus. It is impossible to see how Jehovah can be Jesus, if He is speaking to him.

In the following verse Paul refers to God subduing all of Jesus’s enemies as is prophesied in Psa 110:5 and Jesus being subject unto God. Here again it is made very clear that Jehovah and Jesus are not one in the same person, but that even Jesus will be subject unto God.

And when all things shall be subdued unto him [by God], then shall the Son [Jesus] also himself be subject unto him [Jehovah] that put all things under him, that God may be all in all. (1Co 15:28)

For God [Jehovah] to be Jesus it would be like saying He was talking to Himself. It would take a real stretch of the imagination to concoct a theory that would explain away this fact and make it look like the obvious is not really the case. The trinitarians would have to fabricate some kind of interpretation to explain that one away.

What think ye of Christ? whose son is he? They say unto him, The Son of David.
He saith unto them, How then doth David in spirit call him Lord, saying,
The LORD said unto my Lord, Sit thou on my right hand, till I make thine enemies thy footstool?
If David then call him Lord, how is he his son? (Mat 22:42-45)

What Jesus is actually getting people to think about here is the fact that he is the son of David since he is a descendant of David and Lord ['âdôn] since in this prophecy the LORD [yehôvâh] is speaking to his Lord ['âdôn], refering to Jesus.

In the New Testament: The apostle also references this verse. He is literally saying that David was speaking of Jesus, showing how the Old Testament prophesied of him.

Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear.
For David is not ascended into the heavens: but he saith himself, The LORD said unto my Lord, Sit thou on my right hand,
Until I make thy foes thy footstool. (Act 2:33-35)

Here Paul makes it even clearer that the Psalmist was not speaking of himself but of Jesus, who is sitting at the right hand of God and will be there until his enemies are defeated.

For he [God] hath put all things under his [Jesus'] feet. But when he saith all things are put under him, it is manifest that he is excepted, which did put all things under him.
And when all things shall be subdued unto him, then shall the Son [Jesus] also himself be subject unto him [God] that put all things under him [Jesus], that God may be all in all. (1Co 15:27, 28)

Just like David prophisied, God put all things under Jesus’ feet or gave him complete authority and power and would rule with absolute power until all of his enemies are subdued. That’s when Jesus himself will be subject to God.

It is exceptionally clear here that in both the Old and New Testaments that God and Jesus are completely two different persons, not the same one. It is obvious that Jesus is not a figure of speech or a metaphore to represent God. In the future even Jesus himself will be subject to God. From this it would be impossible to conclude that Jesus and God are one and the same person.

If Jesus and God were the same person, then why does Jesus never specifically say this? And why would both the New and Old Testaments constantly refer to them both as separate and distinct persons if they were actually one in the same person? Why would God go to such lengths to portray a picture that is not true when the reality is something completely different?

The truth is that God never did say or even infer anything of the sort. It is a complete fabrication of a theory created through false interpretations of scriptures many times incorrectly translated.