Hair color trouble? 10 pts!?

So a couple of years ago, I started dying my hair reddish brown (my natural color is a dark, dull brown). Now, I would really like to get it back to plain old brown (maybe like a rich dark brown). The problem is, every time I try to dye it brown, the red shows through in a couple of weeks, and my roots are still dark brown while the rest of my hair is red/brassy! How can I get rid of all the red tones in my hair so I can dye it back to a nice brown and have it stay that way? I really, really don't want to go to a salon.