Place a piece of underlayment and a single plank against the door casing to see if the floor will slide under the casing.
Mark the door casing 1/16-inch above the flooring if it will not slide under.
Cut the door casing at the mark with a back saw or coping saw.
Lay the last plank before the doorway.
Lay the first plank that will go to or through the doorway in place, but do not attach it to the plank before it.
Measure how much (if any) of the plank you will need to cut out. In many cases, you will need to cut a corner out of the plank to fit around the doorway.
Mark where the cut(s) will be on the backside of the laminate plank. Be sure to allow for the expansion gap of 1/4-inch.
Cut the plank as needed to fit around the doorway using a jigsaw or miter saw. Jigsaws will make short work of corners, miter saws are ideal for making larger cuts and cutting the planks in general. If the "tongue" side of the board hits any part of the wall or door casing, cut this off as well.
Attach the plank to the plank before it using the tongue-and-groove method.
Lay out any other planks that go to or through the doorway, making sure to mark and cut any that will need to fit around the doorway.