Lay drop cloths down over the flooring. This will protect your floor and make the cleanup process easier -- especially when it comes to picking up the small nails that may fall during this project.
Set up scaffolding in the room. While you can use a simple ladder, you will need good leverage to remove the furring strips. Scaffolding makes the project easier and gives you more room to work.
Pry off the first furring strip. Insert a pry bar between the furring strip and the ceiling joist then pry downward. Move the pry bar a few inches then pry downward again. The wood should pop off of the nail heads.
Remove any broken furring strips by hand. If the furring strips are very old, they may be brittle and will easily break off with the pry bar.
Take out all of the old nails left behind in the ceiling joists. Use the hammer claw to pull the nails out one by one. If a nail is driven too far into the joist to pry out, hammer it in so that the head is flush with the joist.