When you really want to put paint on a wall quickly, nothing beats a roller. To improve on that efficiency even further, lose the tray and get a 5-gallon bucket equipped with a roller screen. The bucket holds plenty of paint, you won't step in it by accident, and the handle makes it easier to carry than a tray so you can keep it close by. A bucket also lets you "box" your paint—pour like-colored cans into a single container to even out any minor inconsistencies in color.
Using a bucket is easy. Just dip your roller about halfway into the paint and roll once up the screen to squeeze out the excess. One caveat: The bucket and screen must be scrubbed clean after each use, preferably before the paint dries. Otherwise, dried paint flecks—which some painters call "boogers"—will leave lumps in your finish. (If you wait too long, it's time for boiling water and a scouring pad.)
TOH Tip: When you take a break from rolling, wrap the paint-saturated roller in plastic and squeeze out all the air. A roller will stay wet for a couple of days, as long as the plastic touches its entire surface. Just remove the plastic, and you're ready to roll.