Allow the tattoo to heal completely. Even if you immediately see the flaws in the design once the tattoo process is complete, you should still let it completely heal, for two reasons. First, in the time it takes the ink to set, you may begin to appreciate and even love the design for its flaws. Second, you will need to know exactly how the healed tattoo looks before determining the proper corrections or additions necessary to change the design.
Identify exactly what is wrong with the design. If there are minor flaws in color or shading, or even line work in some capacity, simply revisit the tattoo artist and have him make the necessary corrections. If it has something to do with the nature of the tattoo itself, however, such as a significant other's name that is no longer significant, you may need to get a little more creative.
As previously suggested, revisit the same artist if you simply need minor corrections. It may seem redundant to return to the same artist whose work you were not happy with in the first place, but most artists will not work on somebody else's design. That's why it is so important to check an artist's portfolio before getting the initial tattoo. If you just want to cover the tattoo with another, however, you can visit any artist of your choosing.
Explain exactly what is wrong with the tattoo and exactly how you want it fixed or covered. Any artist worth her salt will know precisely how to fix color, shading or line work, or will know just what is required for a "cover-up" tattoo.
Be open to any suggestions the artist may have and make sure you fully approve of the cover-up stencil before the new tattoo process begins.