I've done this a number of times and, as Mary and Agent say, it is quite easy to do. The wood that's used for carpet grippers is quite thin and breaks quite easily. I used a chisel rather than a screwdriver to lever out the gripper rods because I found the angled end was easier to push under the rods, and I could happily bash the handle end of the chisel with the hammer, as that's what they're designed for.
You don't need to be particularly strong to do this, because once you get the end of the screwdriver/chisel under the wood, you're pushing down rather than pulling up, if you see what I mean. Similarly with the claw end of the hammer to get out any remaining pins.
Some tips: Use the fattest, squishiest cushion to kneel on. Use gardening gloves to pick up the removed grippers, the upward spikes are quite ouchy. Most underlay is held in position by staples, so you'll need to check the floor for those, either a screwdriver or a pair of thin-nosed pliers works well. And a container to put removed pins/staples in as you go along.
Just take your time, it doesn't all have to be done in one day. The most important area is around the door and under the window, where people's feet might come into contact with the remaining gripper rods.
It's quite a satisfying thing to do, especially if you end up with a lovely wooden floor.