The "Triangle" of coverage is your friend. You shoot a shot of the two people talking all the way through the scene... then move to one side and shoot an "OTS" (Over The Shoulder) of one of them all the way through the scene, then "Turn Around" and shoot an OTS of the other actor all the way through the scene. Then you line up those 3 takes and cut between them as you like. Having solid dialog from each actor allow you to adjust their timing between lines as well, including overlapping them or spacing them out to add some dramatic pauses as well.
Draw a line through the actors from one to the other and make sure that your cameras always stay on one side of the line (This is the "180 degree rule"). This makes sure that each actor gets their own side of the screen, so when they are cut together they appear to be looking at each other as they're talking.
"J and L Cuts" are used to overlap dialog with a reaction shot either starting the audio before the video, or cutting away from the video before the audio has finished. Not seeing the beginning or ends of lines allow you to linger on a reaction longer or "motivate the cut." This happens when something you've done in the edit makes the audience want the cut to happen when it does... when this happens, the audience doesn't notice the cut.
Generally, if you make a cut just before a piece of dialog starts, it's very obvious that there's a cut... if you wait until the dialog starts before cutting over to the video, the audience is drawn in a natural way. We react by hearing, then turning to look in the real world. If you give them a reason to want the next cut, then give it to them, you create a flow that feels natural to them and they'll be more willing to stay with you for the ride.