"You can generally continue to exercise shortly after you've been tattooed. It is however advisable to wait at least 24 hours and to be cautious about over doing it in the area of the tattoo. Use your judgment - if you feel that your workout is causing you more discomfort in the area of the tattoo than try to avoid that movement. Make sure that you clean down the tattoo immediately after any strenuous exercise and that you go through your full care regime as outlined at that time. " From here: www.divingswallow.com/faq.html
Depending on the area and size the time that it'll take to heal and amount of discomfort will vary. Whoever does you tattoo will give you specific instructions, but overall getting a tattoo shouldn't prevent you from working out for a very long time.