On most mobile phones these days it is done computationally in one click. A modern photo camera often packs enough dynamic range in raw format that it's possible to achieve the effect in one click too. The old fashioned way (that some still swear by) involves taking different photos at varying exposure values and blending them with software specifically for the purpose like Photomatix HDR or in Photoshop. Most of the work with these is choosing an appropriate blending mode in a computer. Lots of sliders and decisions in post. Some cameras have the function of blending different exposures into an HDR straight out of camera often giving not so many choices how they will do that.

With light painting I've grown to prefer single photographic exposures with no editing required.