The races can usually be removed with a hammer and an old flat blade screwdriver that you don't care about.
The head tube races usually come out pretty easily if you stick the old screwdriver down into the head tube until it hits the internal edge of the race. Tap gently once, then move the screwdriver to the opposite side of the head tube. Keep going back and forth every other blow, so that you won't be driving the race out crooked, which could damage the head tube.
The fork crown race is sometimes more challenging, depending on the construction of the fork crown and the width of the race. You may or may not be able to get a good purchase on the underside of the race.
If the race has a good overhang on both sides of the fork crown, a bench vise is often best for this. Open the vise just wide enough to permit the fork crown to fit through looseley, so that the crown race is sitting on top of the vise jaws. Use a mallet to rap on the top of the steerer, driving the fork down and away from the race. It would be a good idea to thread the headset locknut onto the steerer before doing this, to prevent damage to the threads of the steerer.
Alternatively, a bicycle work stand can be used to clamp the steerer with the fork upside down. You can use the hammer and old screwdriver to drive off the race.
Some races and some fork crowns give very little to grab onto. There are special shop tools to work around this problem, so you might want to just bring the fork into your local shop and have them remove the race.