Many people will advocate one-handed typing on a standard keyboard with the QWERTY layout; their main (and only) argument is conformism. That's certainly possible and there's no/flat learning curve. That said, such solution is far from optimal.
A step further is a layout optimized for one-handed usage, so that the user doesn't have to move their fingers across whole keyboard all the time. There are special symbol arrangements, such as Dvorak's one-handed layouts, and there are mirrored keyboards—the user types on one half of the keyboard as normally, and uses the same keys combined with a modifier/toggle, that turns those keys into the respective keys from the other side of the keyboard… that's actually similar to, e.g., the aforementioned Matias Half QWERTY.
And then there's specialty hardware combined with the specialty symbol arrangements. This includes Matias Half QWERTY or Maltron keyboards. Or one half of an ErgoDox.
Alternatively, it's possible to type using something other than a keyboard. See, for instance, Dasher. Swiping on a high-quality trackpad would be another option.