Lay the last row that the intersection is on as you've laid the rest of the floor.
Measure and mark the piece (on the back) where the corner of the intersection will hit.
Cut the piece you've marked so that it fits around the corner but still allows for the small expansion gap if it's a floating floor.
Cut off the tongue of the plank if it hits the corner (if you're installing tongue-and-groove flooring).
Undercut the door casing in the intersection, if there is a door.
Install the piece as you have the rest of the planks (tongue-and-groove, nail-down or glue-down).
Continue installing the floor through the hallway or other area of the room after the intersection. The corner piece is the only one you'll need to adjust for the intersection.