There are lots of ways to do it. What I do is rough up the handle, then apply simple leather dye like I use for sheaths.
How it comes out much depends on how much adhesive is used in the assembly of the handle. Some adhesives won't let the leather take on color (superglue). Some seem to allow a bit of take up.
Get an aggressive foam sanding block from Home Depot. Rough up the surface of the leather to prep the leather for taking up the color.
Dampen the leather handle with a damp cloth. You don't want it wet, just damp. Use a spongy type applicator and apply the dye smoothly all over the handle (I get my dyes from Tandy, they are made for use on leather). I suppose light brown, quality shoe polish would also work.
You can then either let the handle dry, then rub with a cloth, or, what I do is I use a hard smooth object like the handle of a screwdriver or similar, and rub down the surface of the handle while it is still damp with the dye. This polishes the surface and causes the little fibers of leather to fuse together. This helps get rid of the fuzzy look of an unpolished leather handle.
Then what I like to do is apply a coat of briwax to the handle, then buff. If you want to completely waterproof the handle, apply a thin coat of superglue, then buff with steel wool, repeat.
Andy