Priest: The Lord be with you.The dialogue begins with the familiar greeting and response.
Congregation: And with your spirit.
P: Lift up your hearts. Lam 3:41
C: We lift them up to the Lord.
P: Let us give thanks to the Lord our God. 1 Chr 16:34; Jdth 8:25; Isa 12:4
C: It is right and just. Ps 54:6; 92:1; 147:1
P: It is truly right and just, our duty and our salvation...
Then the priest invites us to lift up our hearts, and we gladly do so. This exchange is based on Lamentations 3:41, in which Jeremiah says "Let us test and examine our ways, and return to the LORD! Let us lift up our hearts and hands to God in heaven." This part of the Mass has not been re-translated, although in all honesty it could have been. The Latin is far more succinct than the English we are familiar with.
The priest says Sursum corda which literally means "Hearts aloft" or "Raised hearts"; it needn't be interpreted as a command. Maybe it's a question: "Are your hearts raised?" Maybe it's an invitation: "Let us raise our hearts."
The congregation's response is Habemus ad Dominum which literally means "We have (them) with the Lord." Maybe we're saying our hearts are already raised.
The dialogue ends with the priest inviting us to “give thanks” to God. He's essentially saying, "Let us 'do' the Eucharist." The people's response has changed here; it is simpler, matching the Latin: “It is right and just” has taken the place of “It is right to give him thanks and praise”.
This change is important, because the priest continues to pray the Preface by taking up the very same expression we have just used: Dignum et iustem est, we say, and the priest says Vere dignum et iustum..., “It is truly right and just...”