This is not as simple a topic as would appear.
The first thing I'd advise is to read the hide. Run a damp, but not soaked, cloth or sponge over the piece you want to dye. That will show any blemishes or irregularities that will affect the flow of the dye.
For about fifteen years I have been piling a coat of neatsfoot oil on the leather and then, with wool patch and rubber gloves, rubbing in the dye in broad circles. I like to get the dye right on after the oil because the oil helps spread it. My Old Master used to do this with just water, but I never liked the tactile skills necessary to get just the right amount of water in. Work slowly enough so as to see the dye working in.
Dye will get irregular if the leather is either too dry and soaks it up irregularly or if there is variance in the fibers.
Lastly, and this may sound a little curious, there is such a thing as too uniform. For the most part ( but not always) The factory/ industrial, dead-on even look on hides is more of a product of the nineteenth and twentieth centuries. Just my own prejudice here.
Don't take all this as gospel, either. You'd be surprised how many techniques there are out there and, hopefully, Coyotes like James Rogers, Marcruger and Sligo BIll and other talented craftsmen will pitch in on this thread.