There are many ways of bolt extraction, and none of them are guaranteed.
If there is anything of the old bolt still sticking out above the gasket line, the first attempt is to try to heat it, and let paraffin wax or a rust penetrant wick in to the threads. Then grip the remaining bolt with pliers or vice grips and try to remove it. (don’t try this with regular pliers, if your pliers will not break off 3/8” studs they are not good enough)
It will either come out of break off lower which would bring you to the next step.
If there is not any part of the old bolt above the gasket line you have four methods.
1. Drill a hole of the correct size as close to center as possible and try and easy-out.
1a. some will try heat and wax or penetrant again after the hole is drilled and before they try the easyout
1b. on a personal note, I have found that a spiral easyout works better for me than a straight fluted one. but you have to know your limitations. A straight flute will slip it’s hold if the bolt will not budge where a spiral flute will break off in the bolt causing a bigger headache than what you started with.
2. left handed drill bits. I have a set although they don’t work very often. Not to mention they are expensive. The theory is you use a left handed drill bit to bite in to the bolt as you run the drill backwards and it will force the bolt to turn counterclockwise. Thus, removing it. works maybe 5% of the time. But when it does work, it’s fast and you feel very proud of yourself.
If the stud is in an open shoulder, so you can see the back side of the stud an right handed drill bit might be able to drive the bolt forward
The 3rd and 4th option must be chosen by personal experience, and is mostly a judgment call as to if you want to try 3 or just jump to step 4. you definitely want to try 3 if the bolt is in a thin walled shoulder (like if there isn’t much metal around where the bolt goes in to)
3. center your drill bit as much as possible. Start with a small bit and slowly work your way up to a larger bit. This will let you push sideways to recover if you didn’t have you punch mark centered in the beginning. Go up in drill sizes until you have removed as much of the bolt that you can without touching the threads of the head, manifold or whatever you are working on.
3a. if you don’t know what a Heli-coil insert is, go to an auto parts store and look at a one, and read the back so you will understand where they fit in this universe.
3b. take a very small punch, go over to the bench grinder and grind a curved shape in to it on the very side. You want it as far from the center as you can make it. when you are finished it will look like a leather working tool used for digging out trenches.
3c. use the new punch tool and a SMALL hammer. Start and the upper most thread and walk the spiral out of the good threads in the head, manifold, or whatever you are working on.
3d. clean up any nicks you may have made in the thread with a tap.
4. the final step is a thread insert. I have used 3 different designs and the Heli-coil brand seems to be the easiest to use, it has good results, and removes the least amount of metal from the part you are trying to save.
4a, a thread insert works like a reducing pipe bushing, lets say you have a 1/2" pipe thread and you need to put a 1/8” oil sending unit in it… so you use a reducing bushing. A thread insert is the same idea. You have a big hole and you want to put a small bolt in it.
you start with a small hole and you mess up the threads some how. You want to tap it to a bigger hole but the bolt would be to big to fit through the other part. So you use a special thread insert tap on the big hole. Screw in the new “reducing bushing” and the inside threads of the bushing are the threads you need.
4b. again be careful when working on thin walled stuff.
4c. a helicoil is stronger than the original threads. So don’t be afraid of them.
good luck with it.