I'm naturally brunette and I currently have copper colored hair. I'd like to go back to my natural color, which is light brown. If I put light brown dye on top of the red, what will happen? Will it take or should I go with a darker brown?

I too have light brown hair and dyed it reddish brown. I have died it twice very dark brown since then, and it seems like the red slowly makes its way back through your hair. I condition my hair every single day and take good care of my hair, but when it fades, the red comes back. You should have it professionally done to make sure the red doesn't come back. I know I'm regretting dying my hair red... hope this helps :)

Did you use stuff from a bottle/box combination? I also used to dye my hair black, which wore off quickly and showed up brown after a few weeks. But after having my hair professionally dyed red once, I've been doing it myself and using salon dye I've mixed myself. Would that stay on my hair and not show through red? I can't keep dying my hair - it's pretty much destroyed as it is.

I did all the dying myself just for fun. But maybe wait a while until you dye your hair again and have it professionally died brown (or whatever color you want). My hair got kind of worn out too after dying it so much. If you really want to get rid of it, you can have a salon strip your hair and then dye it the color you want. That way the red will be gone for good.

Using a light brown hair color on copper hair will not make it light brown. If you want to go darker, minus the red tones. Choose as ash color in medium ash brown. But, if you want your natural light brown color back, you can get a permanent hair color remover which will remove the unwanted hair color you have, and then you can re-color your hair to your original color.

Will it actually work, or would it be better to go to a salon? If I get the color remover and remove the red and then dye it to match my natural color, will it actually turn out brown?

I really wouldn't strip the colour to get it lighter.
Stripping your hair puts it in shocking condition and what I found out was that if you strip the colour from red, it goes a bright orange, then you have to keep stripping it and by then it's in quite bad condition.
Then when you dye it the light brown colour, it ends up having green-ish tones and really is not attractive at all, it becomes really really thin too.
I think what you should do is just put non- permanent, mid brown hair dye on it and keep doing that until the colour grows through.
I know it's not ideal and it will take time and patience, but it's the best way to go :)