How should I connect a new outlet with two pairs of wires?
Yes, wire the black wires to the brass screws and the whites to the silver screws. The black wire that is not hot is feeding a receptacle downstream and being fed by the wire that is hot via the receptacle. Do not remove the tabs on the outlet in this case.

If it's a direct replacement, when in doubt wire the new one the same as the old one and you'll be fine. If you have any doubts as to the connection, post up a few pics.