Scan the shelves for hair dyes that are semi-permanent. Semi-permanents are less damaging and are "deposit only" colors. What this means is that, unlike a permanent color, if you use one of these on your brown hair, it will not lift color molecules out of your hair's cuticle. What it will do, however, is coat your hair with a color that will neutralize the green; that's precisely what we are going for here.
Hover over to the brunette portion of the semi-permanent selection and choose a brunette that has a red base. This would be any brunette with the word red or auburn in its name. The brunette that you choose should be at least one shade lighter than your present hair color, in order to maintain your depth of color. In other words, don't choose a brown that is darker than what you have now.
Read the manufacturer's instructions and apply the semi-permanent hair color to your hair. Most manufacturer's recommend pouring bottle "b" in with bottle "a," sealing the bottle and giving it a shake. You can then apply the color to your hair just as you would shampoo. You don't need to make any fancy parts or sections. Just make sure you cover all of your hair with the color. Got it?
Run a wide-toothed comb through your hair, to make sure you get an even coating of color. Leave the dye on your hair for as long as the manufacturer recommends; give your hair a good warm water rinse, until the water runs clear. Slather on a conditioner, rinse again, dry and style your hair as usual.
Anytime you go from light to dark, there is a chance that your hair will pick-up some of the base color in the dye. All "ash" hair dyes have a green base. Applying a hair color filler to your hair before you dye your hair from blond to brown can prevent your hair from sucking in the base and creating the green halo effect.
Red is opposite green on the color wheel, so they both cancel or neutralize each other. If your hair is too red, you can apply an ash to neutralize.
Read the instructions carefully before applying the hair color. While one manufacturer may recommend applying the color to damp hair, another may suggest a dry canvas.