Any time you're going to change the hair more than two shades different than the natural, you're getting yourself into a big, big job. You consider, do I have gray hair and am I covering up my roots? If yes, you should look for a product that looks very similar to the color that grows out from your hair naturally.
You should apply the color onto your roots and follow the manufacturer's instructions on how to cover the gray. My tip is to not put the color on the ends. Put the color on the roots, have it processed, again, for the time the manufacturer's say. Then the last five minutes, you're going to hop into the shower, you wet the ends a little bit, take the rest of the color, you can add a little bit of water, and freshen up the ends for maybe one to two minutes, not much more. Too much after that will have a dark, inky cast.
If you'd like to go lighter, I would recommend staying within one to two shades of your natural color. Look for a hair color that has cool undertones. You're looking for something that's maybe labeled "cool ash brown." It might even tell you it has a blue or a violet undertone. Process 30 minutes, or how long the manufacturers tell you to, and just a few minutes on the ends. Then you'll have a nice, shiny brown.