Are you talking one-handed, weak hand, shooting
double action? That's a very tough combo, so don't set your bar high at first. I started shooting one-handed double action (bullseye style) about a month or 2 ago just for the challenge. Of course, I was shooting using my normal right hand. I've also been practicing 2-handed shooting from my weak side, and now I'm starting 1-handed weak side, double action.
What I found is that my brain already wired correct site picture and steady trigger pull, so I just needed to strengthen my left trigger finger and continue focusing on the fundamentals. My advice, then, in no particular order, would be to:
1) Do lots of dry fire with your weak hand. You'll be amazed at how quickly it'll feel more normal.
2) Slow down when shooting and focus on the fundamentals. It's gonna be darned tough to get any kind of respectable grouping at first, so just slow down and do your best. Speed up only after the group size decreases and your trigger control gets better.
3) Be patient & don't set your bar too high. When I started shooting 1-handed on my strong side, my groups were at least twice my 2-handed group size. Now, they're about equal.
4) As you aim with 1 hand, your hand should be able to keep the sights aligned, but you'll notice your arm & body can't hold the gun steady around your POA, and there will be a tremendous amount of "wobble". Don't try to correct the wobble. You won't be able to, and the only thing you'll end up doing by focusing on fixing the wobble is to lose focus of the front site and disrupting your sight alignment. Just shoot. With time, your arm will get steadier and the wobble will diminish and your groups will get smaller. In contrast, if you go for small groups right away by trying to "fix" the wobble, you'll pick up bad habits that will hurt you later on.
5) Since you posted this in the revolver forum and you mentioned a .22, I'm assuming you have a .22 revolver. If so, great! Look into buying some Aquila Colibris. These are primer-only rounds that have the muzzle energy of an air pistol. You can shoot these outside or in your garage from your revolver. A cardboard box with a phone box taped onto the back makes a good trap. Just a box a day along with your dry fire will help tremendously.
6) What you're trying to do is essentially bullseye shooting. Read up on it. You may not have aspirations to compete or to be as slow and accurate, but the basics of bullseye shooting will help.
http://www.bullseyepistol.com/