Wear. Disposable. Gloves!
Disposable gloves take the "discolored palms" out of the equation. You can take your time and blend well without have to worry about your hands staining. This will allow you to create the most even tan.
Gloves also take water out of the equation, as you don't have to worry about washing your hands and "dripping" over any area you may have already distributed product. If you self tan you already know... when developing a tan, water is your worst enemy!
I recommend vinyl non-latex gloves that fit snugly to the hand. Latex is more "Clingy" so it makes it more difficult to blend your color. You can get disposable vinyl gloves almost anywhere, and at a cheap price.
The risk of "stained palm" is no more! Pick up a box of gloves and never worry again.
Quick tip: I tan the backs of my hands last. What I do, is remove one glove, and tan the back of that hand with the glove that's still on. Then I wait a few minutes, slide the glove back on the now tanned hand (very gently so I don't smudge color) and tan the back of the other hand. I also will use a self tanning brush or mitt occasionally. Simply rubbing the backs of the hands together will distribute some color, but may not distribute color into the creases of the hand (knuckles, etc) for the most natural look.