How? Use a graphics program and export the icon as a .png image.

Icon size? Depends on how it is going to be used.

Any decent general purpose graphics program will be able to produce a .png file. I mostly use GIMP and Krita. Photoshop is a fine choice if you have the budget for it. There are many other options.

Depending on style, program, and intended use, there may be a suitable tutorial. A recommendation would have to be based on a more exact definition of your goals.

Draw, scan, open in graphics program, edit, export as .png, and you have your hand-drawn icon. Alternatively, use a tablet to 'hand-draw' digitally.