As long as you aren't tattooing the same area you've recently done, you can go back in for another as soon as you like.

Having said that, I'd recommend letting the first one heal for a few weeks before you get another. Especially if it's your first tattoo, you want to go through the process of getting inked, healing, and appreciating your new tattoo before you rush into getting another. Once you've appreciated the experience and the result of your first tattoo completely, you'll have a better idea of what you want for the second (and third, and fourth...)

For more information on tattoo care, see the other FAQs on 'How To Take Care of Your New Tattoo.'