Red tones are very difficult to deal with--they fade quickly, but they never fade all the way. And what was once a gorgeous, vibrant red can become a dull chestnut brown you would do anything to get rid of.
When working with tones, you need to remember that all colors have an opposite. Simply dying your hair a neutral or golden brown will not get rid of the red tones. You have to administer a hair color with a tone that is actually the opposite of red--green.
Now, don't freak out. This won't mean you'll have green hair. Some ash toned browns have green undertones, but it's hard to tell which ones do, when we're referring to drugstore dyes. So if you want to go brown instead of red, go to a professional beauty supply store and look for a dye that explicitly states what the undertones are. Find a brown with green undertones and go from there.
If you are trying to go from red to blonde, it's a little trickier. You have two options:
1.) Bleach your hair until it is yellow or white, which is very damaging, but will efficiently get rid of the red tones. Then, color over it with a demi-permanent color in the blonde shade of your choosing.
2.) Use Color Oops in the extra strength formula, and make sure to wash thoroughly. Your hair will probably be slightly orange. Use a high lift blonde color in an ash shade, but keep an eye on your hair to watch for damage.