The problem is that many people take dye jobs into their own hands. This means they have probably picked up a bottle of dye at the grocery store - a bottle which was one of few other choices in terms of hue. It therefore will end up looking very awkward and unnatural, causing many women to dye their hair back. For the best results, you should see a stylist.
Of all the shades of red, strawberry blond is the worst when it is faked. The combination of red and blond almost always turns out to be a horrific, brassy orange. The reason for this is that redheads tend to have multi-colored strands of hair, changing when the light hits it. They have more than just high and low-lights like other hair colors.
One thing many people forget when they dye their hair is to dye their eyebrows as well. This is often an indicator of a faker. Few natural redheads have extremely dark eyebrows. Redheads have light eyebrows, so if yours are already blond, leave them. If yours are dark, try going slightly auburn. You will be amazed at how more realistic the rest of your hair looks if you do this. Just never dye your eyebrows the same shade of red as your hair.
Eyelashes are another way for people to tell if someone is faking their hair color. You can always get your eyelashes dyed at a salon, but it may just be easier to go for mascara of a different color than you usually get. Look up makeup specific for redheads--it is a growing market. You can then get dark auburn mascara which will look less harsh than black.
Keep in mind that your skin coloring has a great deal to do with how realistic the color looks. If you have pale skin, you are more likely to look natural with it. Pick a pale shade of red. In this case, you will be able to get away with wearing just about any shade. If you are darker or have heavy freckles, light red hair might look silly. Go more the russet route and stay away from red clothes.