Alex,
I use a syringe. I heated the end to make it flat, then filed it down a bit to allow it to squeeze into the slot.
Clean-up is pretty simple wipe most of the unused glue from the body and put a small wire in the bottom followed by spritzing some water in there to make it kick. When it dries just snap it out.
The plunger needs to be wiped clean with paper towel. I've been using the same syringe for about two years or so.

The glue will foam out of the slot as it kicks off but won't stick to covering or the hinge with vaselene on it. I use pliers to snap off the big globs and a pointy awl to chip out the remainder leaving a nice clean hinge.