Dyeing leather shoes a darker colour is easy and can be done with materials that cost just a few pounds. Bear in mind, you will not be able to dye rubber or plastic parts, and dyeing works well only on smooth leathers, not suede or nubuck.
Before shoes can be dyed, they must be cleaned of all dirt, then a deglazer is used on every surface and seam. Deglazers remove waxes and finishes, and prepare the leather for dye.
Dyes penetrate the leather, rather than coat its surface. Dyeing a shoe while it is wet with deglazer allows speedier, deeper penetration.
You'll get better results by dyeing light shoes an interim colour, then your darker colour. Dye manufacturers recommend dyeing white leather blue, then black; or light green before deep brown.
Cobblers sell spray cans of leather paint, but paint is better suited to renewing a colour than covering it.
Paint is useful for man-made soles or other pieces on a shoe, which will not accept dye. Still, you will have to renew the paint job periodically.