Before you ever apply any kind of foundation over your tattoo, you should first color correct. Color correcting is the process of applying a concealer that is opposite in color of your tattoo according to the color wheel. Here is a cheat sheet for you:
If you're having trouble covering a black or blue ink tattoo, try color correcting with a peach colored concealer.
If your tattoo leans green, try color correcting with a highly pigmented red lip liner or red lipstick first.
If it is red, use a green concealer. (You can also use green concealer to correct any skin redness issues that you may have, such as acne or rosacea.)
If it is yellow, use a purple lipstick (or vice versa).
Of course, depending on the undertones in your skin, you may have to do some adjusting when it comes to what shade of green, peach, yellow (etc) concealer will work best for you.
Once you have lightly applied a color correcting concealer, dab on (with a buffing brush or your fingers) a few drops of a foundation that is specifically formulated for covering tattoos, such as Dermablend Leg and Body Cover or Kat Von D Lock-It Tattoo Foundation. It is very important to work in layers and blend, blend, blend! If the first layer isn't doing it for you, set it with a layer of translucent powder, let it sit for around five minutes, brush off the excess powder, and add another layer of foundation until ideal results are achieved. Finish with a translucent powder (ex: Laura Mercier) and a setting spray (ex: Urban Decay) for long lasting results.