What is the easiest way to measure an irregular floor space?
If they'll accept a full-size model, use the technique for making a template for cutting vinyl flooring to the right size and shape (taken from another answer of mine):


  ... I use a roll of craft paper and sticky tape to make a template of the room. Start in the center of the room, lightly stick a strip to the ground, and cut it at the edges of the room. You get a cleaner edge by going a little past the edge, then folding the cut edge back and sticking it down with the tape. Keep sticking more strips to the template until you cover the entire room.


If they want a smaller-scale model, use a T-bevel or angle finder to measure the angles in the corners and careful measurement to get the lengths of the walls. 


Pick one wall as the baseline, scale it down appropriately and make a line of that length on a piece of paper. Write down the original measurement too.
Measure the angle at one end of the end of the wall, and transfer it to the paper at the appropriate end of the line from step 1. Write the angle you measured next to the line.
Measure the length of the next wall, scale it down and draw it at the measured angle from the end of the first line.
Repeat until you've gone all the way around the room.


To verify your accuracy, measure the diagonals going across the room and compare to your scale model.