MY TWO CENTS WORTH - What you have heard, including the previous post, is
true to an extent. However, I usually do not stain prior to gluing,
especially with slabs, table tops, etc.
I usually wipe THOROUGHLY with a wet rag (wet, not just damp). Idea is to
get the surface around the joint good and wet, dilute the glue and get it
off of the project. Then follow with a dry rag to remove the moisture and
diluted glue. Yes, this will raise grain on some woods but not much if done
Invariably you will have some additional glue come up during the drying
process - let that set and scrape it off gingerly with a sharp chisel.
Occasionally if I do not get a lot of runout from the joint, I just let it
set and scrape. Also, I am usually inclined to just scrape the bottom of a
slab glue up because the glue is more likely to form drops than pool.
Another thing to keep in mind is cover your joined surfaces with glue but
don't overglue. The jury is always out on applying glue to both surfaces,
but good coverage of one surface is probably enough. Then clamp the pieces
together until they are joined and quit tightening the clamps. Over
clamping reduces the glue in your joint and adds to the mess.
All of this amounts to glue philosophy that usually gets modified when you
are up to your wrists in glue and the phone rings.