How to remove old barrel with half key snapped in barrel

You will have to get to the ignition by removing the steering wheel and going into steering column.
If you have air bags, dis-connect battery first.
I have no way of telling you how much you will have to remove to get to the ignition lock. I do not have a manual for the car. Generally, you will need a steering wheel puller for the wheel. Then you will need to be careful as there are sometimes, "Free Bearings" that are in collars around the steering shaft that you will be pulling out. Free bearings are bearings that do not have a race or cage to hold them together. So, when you remove the collar or switchplate off of the steering shaft, be very careful to keep them together. You can use axle grease on them to try to keep them stuck in place and to each other.
You will get to the back of the lock and will have to work it out of place or at least turn it to remove it.