Often the pieces that are broken of, are broken along the grain, if the broken of piece is missing then I flatten (straighten)this with a sharp chisel or plane.
Pieces in the middle stop on the end of the break and here I culminate the pieces with a gentlemen's or dovetail saw if possible under an angle as close to the direction of the grain as possible.
Certainly never square to the grain, always the lowest sensible angle.
The reason for having followed the grain where possible is two fold. Not only does it make the join as invisible as possible but also a flat piece of wood will fit onto this. Thus al we have to do is fit the end to the sawn end of the broken away piece.
Sliding this flat bit (leave it as long as is handy )along the flat area up to the end so that with a pencil you may mark the timber of the approx. angle. Cut it along the marking and slide it into place to fit it.
If this doesn't fit then the angle can be adjusted by planing it to fit or if the fit is close but not perfect the clam or stick the piece in place with masking tape and then carefully saw through the offending join.
This will make a parallel gap so that you may now slide the piece up to see a better fit, if it is still not perfect then repeat this process until it is.
Having a piece that fits but is much larger then that which is required was the aim.
You may now mark the piece as to its final shape or simply cut it to length, glue it on and then plane it to size.
I most often prefer the latter as it is easy to plane the piece to size, one can even saw off most of the excess but as the piece is properly fastened this is easy.
Where if one cuts the piece to exact size before hand, a wrong cut wastes all the fitting one has done also the piece only has to slip a little bit during gluing to become useless.
Leaving plenty of waste timber on the piece during gluing often enables one to clamp or tape the piece easier in place.
I always use a strong epoxy such as
or Araldite K 106.
For the advantages of color, gap filling, substrate strengthening and ease of clamping.
I always leave al the pieces larger and stick them to the job with sticky tape during the day.
Then before leaving I glue all the pieces of that day in one short gluing session.
The the next morning I start by removing the clamps and work up al the pieces to the correct shape and start making the next lot.