Above, I maligned some other instructors -- albeit anonymously -- for their lack of understanding when it comes to DA/SA pistols. I've experienced this first hand many times. Especially during my employment with Beretta and SIG, I had opportunity to attend quite a few training events where experienced and/or famous instructors regularly bad-mouthed the DA/SA system. For the most part, the single biggest common trait shared by those people was that they put all of their personal effort into shooting cocked & locked or striker-fired guns. Even the ones who carried DA/SA pistols on duty would regularly opt for Glocks or 1911s for their off-duty guns, their competitions guns, etc. In other words, they didn't put as much effort into mastering the DA/SA as someone who used one exclusively.
One of my favorite stories involves Ernest Langdon, myself, and some other accomplished shooters attending a private 3-day pistol class from a well known instructor and competitive shooter. Every single student in the class was shooting either a Beretta or a SIG. The instructor, who favored 1911s and Glocks, began class by explaining how the DA/SA was impossible to shoot well and even went so far as to recommend shot-cocking the pistol on the draw, throwing the first (DA) shot into the dirt as fast as possible so as to get to the easier (SA) shots. Listening to the interchange between the instructor and Langdon for the next 30 minutes was one of the highlights of the class.
Nonetheless, with the benefit of some DA/SA-specific training, it's fairly straightforward to master the gun as compared to SFA or other actions.
Get confident with the DA shot. If you read that and thought "no duh!" then skip to the next section. But the single biggest problem I see is with people who put far too little effort into the DA part of the DA/SA combination. They load the pistol, keep it in SA mode, empty the magazine without ever decocking, and repeat... never once firing a DA shot. Try to shoot long range groups DA-only. Shoot doubles (first shot DA, second shot SA, then decock) whenever you're doing serious marksmanship work. That longer, heavier trigger is teaching you excellent trigger control. Take advantage of it. Get confident that you can hit what you want regardless of whether the hammer is down or back on your pistol.
Corollary: never be afraid to decock. When I run a DA/SA gun, I decock whenever the gun comes off target with no immediately obvious target to engage next. In other words, every time I "dismount'" the gun and it moves from extension to my ready position, I decock. This follows through even into my practice. Unless I'm starting with my finger on the trigger and the gun aimed at a target (or something simulating a downed threat), every single repetition of every single drill begins with a decocked hammer down DA condition gun.
Corollary to the corollary: make decocking a habit. Whenever I hear an instructor complain that DA/SA guns are trouble because people forget to decock before holstering, I roll my eyes. The best way to fix that problem is to take the ritual you've already created for putting your gun away and purposely changing it through slow conscious repetition. When I'm on the range with new shooters -- or shooters who are having problems remembering how to operate their guns safely -- I don't say "holster." I say "decock and holster." When I'm running a DA/SA gun myself, I never think "holster," either. I always think "decock and holster." If you make decocking the gun part of coming from extension to the ready/transition position as discussed above, it's even easier. And if you ride the hammer with your thumb as you holster, you'll have immediate tactile feedback if you forgot to decock.
Practice the press-out. The press-out was literally developed around DA/SA guns. Not only will it make you faster from the holster and your ready position, every time you practice the press-out you're getting in another rep of working the DA stroke for an accurate shot. (if you don't know what a press-out is, follow this link)
Practice the reset. People talk about the DA-to-SA transition but really if you think about it, every single time you reset the trigger it is going to SA mode. So once you learn how to reset the trigger properly, you always follow that up with a light, short, smooth SA trigger stroke regardless of whether the previous shot was DA or SA. While a lot of people get wrapped up on trying to guarantee they reset as short as possible, the most important thing is to maintain contact between your trigger finger and the trigger throughout the string of fire. When people let their fingers move all the way forward to where the trigger would be in DA mode, they lose contact with the trigger and become far more likely to slap it on the next shot.
One particular drill that I find very helpful involves shooting pairs but at different targets. For example, put up a pair of 3x5 cards a few yards away. Fire a DA shot to the first card, then a SA shot to the second card. Be sure that you maintain contact between your trigger finger and the trigger throughout the entire 2-shot drill, from the moment you begin to press the DA shot all through the reset and transitioning to the next target and through firing the SA shot. Repeat ten times. You should have a 10-shot group on each card. If you're struggling to keep them all on the card with the DA shot, slow down. Practice, work it out, and make it work.
Drilling short bursts from the ready (2-5 shots maximum), always beginning in DA mode, is another great way to habituate yourself to a consistent short light-pull reset. This works your press-out, your DA marksmanship, your reset, and your SA marksmanship.
Don't get frustrated. In a world of Glock shooters, it can be difficult to keep your faith in a DA/SA gun. Every time a Glock shooter beats you at a match or in a drill at class, someone will tell you it's because you've got a DA/SA gun. But when you beat someone at a match or in a class, no one will say "it's that DA/SA gun, it's an unfair advantage!" No, then it's skill, etc. Well guess what? It's always skill, etc. And if you want your skill, etc. with a DA/SA gun to improve, you need to commit and focus and practice.