You can take advantage of this opportunity to put new strings on your guitar since you already have to remove them to replace the guitar nut.
This will help free the nut from the lacquer and any glue that may have been used around it to prevent chipping and breaking of the wood around it when you knock it loose. Be careful when using a craft knife not to cut yourself.
The wooden block will help distribute the pressure of your hammer blows to knock the guitar nut loose all at once and avoid damaging the wood around it.
Ideally, this will only take 1 light tap. If the guitar nut doesn’t come free after 1-2 light taps, try scoring around the edges more with your craft knife. Don’t try to make it come loose by swinging the hammer harder or you might damage your guitar.
Keep in mind that the strings need to be able to clear the first fret so they don’t buzz against it. Try to compare your new nut to the old nut and make it approximately the same height if the old height was good. When in doubt, a little taller is better than too short. You can get new pre-slotted drop-in guitar nuts online or at a music store.
Remove only a small amount of material at a time from the nut. If you remove too much, the slots of the guitar nut will be too close to the wood of the fingerboard and the strings will be too close to the first fret. Evenly sand the ends of the guitar nut if there is any overhang. Remove only a bit at a time until there is little to no overhang when the nut is resting in the slot.
It’s not recommended to use permanent glue, such as superglue, to attach a guitar nut because it will make it very hard to remove and can result in damage to your guitar if you ever want to replace it again.
If you are reinstalling the old strings, this would also be a good time to clean them.
You can check the height of the strings by pressing down on the third note of the top string and seeing if there is a gap between the string and the first fret of about 25 mm (0. 010 inches), or slightly less than the thickness of a credit card. If so, then your strings are resting at a good height.
