With the advent of the soundport, the standard of workmanship inside the guitar body is more easily scrutinized and there's perhaps an even greater incentive to clean up surplus glue as the various component parts are assembled - not that I've neglected this previously. If some vintage instruments can be taken as a guide, it seems this wasn't always a priority, even for well-respected manufacturers. Times change though, and as I inspected a new Martin in a local music shop not long ago, I must say I was impressed by the meticulous attention to detail within the guitar body including the fact that all traces of excess glue had been carefully removed from the intersection of the back plate with the linings and back braces. I vowed then and there to emulate this in my own instruments to the best of my ability in recognition of the fact that it's often the little things that make a big impression.
There are several approaches to cleaning up excess glue once clamping pressure is applied to a freshly-glued joint. Regardless of the method used, I always try to plan ahead and give some thought to the arrangement of clamps to ensure unhindered access to glue squeeze-out after they're in place. I'm also careful not to apply an excessive amount of glue in the first place. A 1-inch foam roller is helpful in that regard, with the added advantage that an even coverage of glue is more quickly and easily achieved.
I know that the preferred approach for many builders, whichever glue is used, is to leave glue squeeze-out undisturbed, letting it partially set or gel before attempting to remove the excess. I use Titebond for the majority of gluing tasks, and find that a flattened plastic drinking straw with the end cut at something like a 45 degree angle is a good first step towards removing unwanted glue as soon as clamps are in place. This approach works particularly well when gluing braces to the soundboard or back. The straw is pushed cut-end-first along the freshly-glued joint and much of the surplus glue finds its way inside the straw which is then discarded. It helps of course to have several pre-prepared sections of drinking straw on hand. Chisel-shaped slivers of spruce or cedar, moistened Q-Tips (cotton buds or ear buds) or a moistened sponge can also be useful as a follow-up and, using a combination of these methods, it's usually possible to remove every last vestige of excess glue without compromising the joint itself.
When gluing braces to the back and soundboard, I exercise patience and generally glue one - or perhaps two - braces at a time. Not only does this slow and steady approach give me ample time to clean up after myself, but I have the luxury of a clear view and unobstructed access to squeeze-out.
Another strategy which contributes to a clean look inside the guitar body is to attach the rim assembly to the back first, rather than to the top. I find it helpful to have a second chance to tidy things up before the top is attached and while the various nooks and crannies which will remain visible after final assembly are still easily accessible.
Cheers
Pete