I am doing a custom cabinet with 1/4 inch quarter round around the openings in the cabinet. I think a nail or brad gun would split the molding. Would glue be acceptable? If so, what glue would be good to use that will set within a minute so that all the pieces can be fitted together without multiple clamps? One site mentioned liquid floor adhesive.
I've tacked it just fine. The trick is you need to use small enough brads. I've found #18 brads split most of the time, and #19 brads behaved well. These were pre-cut, pre-fit and pre-painted 2 coats primer and 2 coats topcoat with a $200/gallon LPU, so you bet I wasn't going to tolerate any splits!
I used an old fashioned hammer and nail-set. These were windows, and the price of a "miss" was a broken window, so I wasn't going to fool around with a machine I was unfamiliar with, doing a craft I wasn't practiced in.
I tried a spring nail-set. It was slick, and drove the #18s lickety split. I'll take that. You can keep your power tools. This thing is the size of a pencil and fits in my toolbox. You can't put a power nailer in your toolbox.
You really need the feel of doing it by hand. That's what educates your brain about the "feel of it", i.e. how wood actually works.
Having just finished doing some cabinet work in my kitchen, I used a variety of methods to attach the molding. Tacking it in, like Harper does, works great and is a quick, one-step operation. I pre-drilled the molding to further avoid splitting. Where smaller lengths were needed I used some fast drying construction adhesive, readily available at home stores. I also found that Weldwood contact cement works great to. Like jack stated above, be careful of using glue if you're going to stain later as the stain doesn't like glue. If possible, stain first, then assemble.
I went out and bought a pin nailer, which shoots headless 24 or 26 gauge brads just for this kind of trim work. Need to use glue or some kind of adhesive as the headless brad has very little holding power on its own, and mostly serves to hold the trim in place until the glue sets up. Nice part is that the hole it leaves partially closes up (since there is no head) and so in many places you don't have to go back and fill in the holes.