Not-very-handy wrote in message
...

Greetings, amigos y amigas

Well, we had a lively dinner party last week!
One of the chairs collapsed under a BIG guy.
Fortunately nobody hurt, and chair seems to be
repairable.

Now I need to know how to extract the broken-off
pieces of dowel from their holes, so I can repair
chair with new dowels.

Also, is "ordinary" wood glue sufficient to glue
in the replacement dowels, or do I need to
get something special.

Recommend rec.woodworking for actual answers, but in the interim- (and IMHO,
of course), if this is a nice or heirloom chair, I'd take it to a furniture
repair place for an estimate, if your town has one. If I wasn't an expert
woodworker (and I'm not), I'd only try DIY on a chair that I could live
without, or live with it turning out ugly. Busted-off dowel stubs usually
have to be drilled out. The dowels usually aren't separate, they are usually
the actual ends of the legs, spindles, cross pieces, etc. Only usual
exception is if all those items are square-section. Second problem- the
holes in seat board, legs, etc, are often not 90-degree angles. Almost
impossible to free-hand drill out successfully, leaving a nice tight hole
for the new dowel. If the dowel is actually the end of the leg or spindle,
grafting a new dowel in there is often impossible. Sometimes it can be faked
by gluing the broken ends, and adding a countersunk and puttied screw
through the center, from the far end. Often, you have to actually recreate
the broken part. This is artisan-level work to make it come out strong and
pretty, and expect to pay accordingly. If you can match the chair style at a
new or used furniture place, that will probably be cheaper.

So, unless you already have a tilt-table drill press, strap clamps,
mortising bits, etc, and a lot of patience, the odds of a successful DIY
repair are less than encouraging. As to glue, I'd recommend Gorilla Glue.