There are several ways to remove broken manifold bolts. A lot of this depends on how much of the bolt remains and is protruding out of the head. If there is enough to grab, some good penetrant should be used first. Use a small vice grip or a socket type of easy-out bolt extractor. These are available from many tool stores or Snap On, Matco and the like.
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Before trying to extract the bolt, use a centre punch chisel and a small hammer to gently tap on the centre of the bolt with just enough force to break it loose. If the bolt is broken off level with the head, then after some penetrant, use the centre punch chisel and make a good dent in the centre of the bolt to keep the drill bit from walking.
Try a reverse direction drill. Many times this works well because it grabs enough as it begins to drill and the friction walks the bolt out. If that fails, then you'll have to use an easy-out. Use a standard drill of the appropriate size, and after making a dent in the centre of the bolt with a centre punch, drill a hole in the bolt as close to 3/8 inch or a little deeper, if possible. Before using the easy-out, spray the bolt one more time with penetrant, and then use the centre punch to tap around the outside edge of the bolt to loosen as much as possible. Walk it out a little by tapping with the centre punch in a counterclockwise direction.
If it is still not coming out, then install the easy-out into the hole in the bolt. Take care not to put so much pressure on the easy-out that it breaks, making it extremely difficult to drill the bolt any further. Easy-outs break easily and without warning, so if it is being difficult, stop twisting the easy-out and remove it. Tap the bolt counterclockwise again, then spray some penetrant and try the easy-out again.
After doing this for several times to no avail, it is time to drill it out. Measure a good bolt. Find a drill bit just a little smaller than the measurement of the good bolt. Keep using penetrant in the hole as it is drilled to save the drill bit from dulling. Then take a reverse drill bit and try once more to walk the remaining threads out. If that fails to work, use a tap and run new threads, which will remove the rest of the threads from the bolt. Run the tap in a little and then out to release the material. Keep it lubricated.