How can I train my left hand to not be completely useless?

You might find your left hand does more than you think. Try not using it for a while. Put it in a pocket, tuck it in your waistband or don't put your left arm through a sleeve and keep it and the hand inside clothing.

Pay attention to how often you're frustrated because you've been using your left hand for ancillary work all along and now you can't do any of that.

Ancillary work is often as important as the main task.

And part of the problem with trying to use a non-dominant hand for a dominant task is that the dominant hand also has little-to-no idea how to do the supporting non-dominant work properly.

NB: If you do decide to artificially gimp your left arm, however, uh, 'armlessly, do take care not to fall over or have some other kind of mishap. At the first sign of tempted fate, ungimp that arm.

Edit: With apologies to those rare folks with only one good arm who have been getting by without any kind of ancillary arm help for a significant period of time, and with genuine sympathy for those who've recently actually lost the use of an arm.

Use it more. That really is the answer.

No bullshit, not a joke. Try masturbating with your off hand.

It is a simple enough task, it gives an (eventual) reward for the work, and it helps build coordination between the muscle groups involved. It's also enough effort that the muscles involved strengthen, and the brain has a chance to build up connections to manage that.

Seriously. It works. I had multiple patients over the years that gained benefits in learning to use their off hand after strokes (heh) or amputation. Same with friends and acquaintances in disability support groups. They'd be struggling, doing their physical and occupational therapy, but eventually run into the horny wall. Things would be difficult with masturbation at first, but it drove improvement in other areas way more than any other task.

Works for men and women (though sitting with a support group slowly working their way around to talking about it was hilarious. The blushing and euphemisms were numerous).

Truth is, anything you'll do often enough that engages all those muscles and the brain will do the same thing. But what tasks are more enjoyable than masturbation? You gonna be chopping onions left handed regularly? Maybe whisking a nice lemon curd daily? Repetition is what builds the kind of dexterity your main hand gets.

A few months of spanking it off handed, and you can try writing, or relearning an instrument. You probably won't ever be as good as with your primary at anything, but you can get good enough to handle daily tasks.

Bit late, but my unintentional solution to this was playing Guitar Hero and, before I had a computer capable of running it and a plastic guitar, the open source clone Frets on Fire. I noticed a massive improvement in dexterity after a few months and it is permanent.

I learned to use my right hand for a lot of things when I broke my (dominant) left arm playing rugby, but I can't say I recommend it as a course of action. Putting socks on one handed was a notably infuriating process.

Just agreeing to use. I was somewhat ambidextrous as a kid, I'd reach with either, draw with either, etc, but at some point just defaulted with my right and now I'm not at all.

learn new dexterity skills. use your phone left hand only. writing.