I have made birria before under the guidance of one of my friends.  It
is a very long process, but worth the effort.
 
If I remember correctly, you should go to get your goat (a young one is
best) as fresh as you possibly can get from a butcher (I went to a Greek butcher
and actually picked it out).
 
You bring it home, cut it up, boil it with salt and bay leaves. When it is
done, you place it in the fridge for cooling along with the broth.  The
broth gets really greasy, so the next day, you scrape up the grease and throw it
away.
 
For the sauce, you will need the following:
fresh tomatoes
mexican oregano
salt
black pepper (whole ones)
garlic
onions
some of the broth from the cooked birria
 
Cook the tomatoes, saute the onions and place in blender with the
broth.  Add the spices.
 
Then place the cooked birria in a pan and add the sauce (reserve some of
the sauce to place on top of cooked birria when serving).  Place in the
oven, garnishing it with fresh onions.  Let it heat up thoroughly and serve
with frijoles de la olla.
 
The "salsa" should be made with the same spices - I use chile de arbol
or the smaller chile (pequin?) with some vinegar and tomatoes.
 
I know I didn't give you the exact measurements (because I just
"eyeball it") - but when you find a recipe, try to keep what I use in
mind.  It is really delicious and worth the effort/time.
 
Esperanza