Here Peter quotes a passage that David wrote in a Psalm which relates to Jesus's crucifixion and resurrection. Since Peter says that David said these words about Jesus, the words "I" and "my" refer to Jesus and the words "Lord" and "he" refer to God.
The context makes it plain that this is an elliptical way of saying that David was speaking as if David were the Messiah. Alternate translation: "For David spoke these words as if he were the Christ: 'I saw"
"in front of me." Alternate translation: "in my presence" or "with me" (See: [[rc://en/ta/man/jit/figs-synecdoche]] and [[rc://en/ta/man/jit/figs-idiom]])
To be at someone's "right hand" often means to be in a position to help and sustain. Alternate translation: "right beside me" or "with me to help me" (See: [[rc://en/ta/man/jit/figs-synecdoche]] and [[rc://en/ta/man/jit/figs-idiom]])
Here the word "moved" means to be troubled. This can be stated in active form. Alternate translation: "people will not be able to cause me trouble" or "nothing will trouble me" (See: [[rc://en/ta/man/jit/figs-activepassive]])