If you don't own a trim bar, which is a very small pry bar (about 6-7"), make the purchase. It's less than $10, and you'll find a 100 other uses for it, but it's perfect for this project. You'll also need to have a an old metal putty knife on hand, the broader the blade the better (you'll ding and dent this, so don't plan to use it again for putty, spackle or drywall). And old metal kitchen spatula will also work, as long as it's solid and not slotted.
First, slide the putty knife under the wood strip (called Tackless), and jiggle it up and down if necessary to make a space just large enough for the trim bar to slide underneath the Tackless. Keep the trim bar positioned on top of the putty knife. When you pry back against the Tackless to lift it, the putty knife will protect the floor from the trim bar making gouges and dents in the wood.
Do wear gloves for this project, and get yourself a stout cardboard box for disposal of the Tackless. This stuff can give you some nasty pokes when you handle it, and will tear right through a plastic trash bag (you don't want to make a Tetnus shot part of the project!) Have fun, and hope your floor turns out beautifully.