Cut the door casings at a height where they will rest just on the hardwood floor, using a jamb saw.
Mark the corner on the back of the planks that you'll fit around the doorway corners so you have a template for cutting them properly.
Cut the corners and any needed cuts on the plank with a jigsaw, a miter saw or a table saw. Jigsaws work best for smaller cuts.
Lay the cut planks around the corners and through the doorway, and continue through the adjoining room.
Lay the last plank before the plank that fits through the doorway.
Draw a mark on the floor where the middle of the door is when it's closed.
Draw another line that accounts for the gap needed between the two floors for the transition molding. This will vary depending on what floor you are transitioning to, as the different moldings require different amounts of space.
Cut the final plank so that it fits between the mark on the floor and the last plank you laid.
Install the transition molding in between the two floors. This is generally done with nails or screws made for the subfloor material and construction adhesive.
Lay the last plank in the hallway so that it ends just under the middle of the door when it's closed.
Lay the floor in the room making sure that the opposite end of the planks will meet up perpendicular to the hallway boards. For example, if you have the groove facing out from the hallway, make sure the tongue of the boards in the room will face the hallway so you have a firm connection.
Continue laying out the floor in the adjoining room as you have started.