The CELTA is an initial teacher training certificate that gives candidates an overview of some of the principles and methods used in teaching EFL as well as six hours of observed and assessed teaching practice. The DELTA is a course for experienced teachers who want to update their teaching knowledge and improve their practice.
So the short answer is that neither the CELTA nor the DELTA will train you to teach IELTS or TOEFL. To get experience you need to find a school willing to give you a class or two and hold your hand through the process. If you familiarise yourself with the exams beforehand, you might have more luck persuading schools to take a chance on you.
For more information on IELTS see http://www.ielts.org/
, and for TOEFL go to http://www.ets.org/toefl