The missionaries will say that Psalm 110 'proves' that Jesus is the Messiah, because Psalm 110:1 tells us the Messiah exalted to sit at G-d's right hand and Mark 16:19, Luke 24:50-51, Acts 2:33-36, Heb 10:12-13, and Matt 26:63-65 all claim that Jesus sits at G-d's right hand.
The Reply is: First of all, this is not even a Messianic prophecy, but a Psalm about David. David, you may recall, was the annointed (Heb mashiach) king of Israel. The verse says "And the L-rd (The 4 letters of G-d's name) said unto my lord (L'adoni, an address here for a human master, in this case David) "Sit at my right hamd while I make your enemies your footstool" "
As I said in parenthases above, adoni is used also as a title of respect when addressing a superior such as a king (see Gen 23:6, 1 Kings 2, 17). To sit at G-d's right hand is an honor G-d simbolicly gives to David at a moment when the neighboring nations were hostile to him. See 1 Chron 28:5 and 29:23.