Use a sheet of typing paper for your target.
Start close and shoot as fast as you can while still keeping ALL your shots on the paper. Work on increasing your speed but don't let shots fall off the paper. If you need to move it back toward you a bit then do it.
When you're going about as fast as you can pull the trigger and the groups start shrinking toward the middle of the paper, move the target out a little and try again while shooting at the same speed. Keep moving it out until you start dropping them off the page and then move it back towards you a bit.
Practice at the new distance until the groups start shrinking again and then repeat the above step.
Don't expect huge improvements overnight. This may sound simple, but it's going to take a LOT of rounds to get good.
Keep repeating the process until you're satisfied with your proficiency or until you can't move it any farther and still keep your speed up.
I'd say that when you can empty a stock centerfire service pistol class handgun at 10 yards as fast as you can pull the trigger and not drop any shots out of the kill zone (say the 9 ring on your target) on a silhouette target you're doing pretty good.
Work on a smooth trigger pull and concentrate on the front sight, not the target.
Then you can start practicing reloads and malfunction drills.