Being able to manipulate your handgun with either hand can save your life in a tactical situation.
Humans are all about comfort. We do what we like to do, and what we are comfortable with. If something isn't comfortable, or just doesn't feel right, we aren't really inclined to do it. This includes handgun shooting.
We all have a favorite handgun, and a particular way we like to shoot. Myself, I prefer a two-handed grip in a modified isosceles stance, but that's just me. However, even though that's what I like, I still include a good amount of one-handed practice in my training.
A correct two-handed grip is without question more stable and effective when using a handgun. This being said, there are some situations where you may only have one hand available.
You may have in your other hand, especially at night, a flash lite or phone. You may be inside your home or office, flipping light switches or turning doorknobs. You may be pushing a child or loved one away from a threat, or keeping a pet from charging into a bad situation. It may be that you are returning fire from behind cover and can only do so with one hand without exposing yourself. In a more extreme situation, you may have your other hand incapacitated.
If you think about it, odds are better than average you will only have one hand able to manipulate your firearm.
And if you aren't training for that, you aren't training.
How much is the Minimum?
Ideally, you should shoot at least four times a year, or every 90 days to maintain the basics of your marksmanship. Every time you practice, at least some of it should be one handed.
For instance, if you only shoot one 50-round box of cartridges, at least 8-10 rounds should be with your strong hand only. Another 4-8 should be with your off hand only. The rest of your fire can be two-handed, but keep a close eye on your one-handed practice. If you see that your one-handed shooting is particularly bad, then it is easy to understand what you need to work on and where you need to budget your ammunition towards.
Additional issues to train on away from the range with an unloaded and safe weapon are how to reload your firearm one handed. If using a semi-automatic, the most common method is to brace the locked back pistol in your opposite armpit and insert a magazine with the functioning hand. To chamber a round drop your slide stop if the slide is locked back, or catch the edge of the slide on solid edge like a wall corner or shoe heel and rack it push it until chambered.
Problems shooting one-handed
Sometimes I find that shooters who have never fired a handgun from their offhand cannot properly manipulate the firearm. Sometimes they cannot even pull the trigger. This is something that needs to be addressed immediately. If you find this is the case then work on it a few minutes a day with a grip exerciser (they are about $10 and can be found at any sporting goods store in the exercise section) until your grip is strong enough to hold and fire your chosen weapon with your off hand. You can also practice with an unloaded weapon and a snap cap safely at home. Finally, if you still cannot operate the firearm safely from your off hand you may want to look at other options such as a smaller weapon or one with a lighter trigger pull.
What to do with the other hand?
When you are firing a handgun one-handed, this presents the obvious question of what to do with your other hand. Most one-handed shooting situations are caused by having something other than a firearm, such as a flashlight or phone, in the other hand. If this is not the case, such as if firing from extreme cover or one hand is injured, I suggest crossing your chest with the free arm, and making a fist of that hand.
Because of the way the body's sympathetic nervous system functions, clenching the unused hand provides an increase in body strength to the weapon hand. In addition, placing the arm across the chest both keeps it away from an assailant who may reach for it, and provides additional ballistic protection for your vital center mass. Furthermore, if your unused hand is injured or bleeding, keeping it elevated above your heart can help with blood loss.
It is all very simple to do, and simple to train with, and if you are not then you truly are swimming at your own risk.