I would like to create a table that looks/behaves like the one to manage fields when editing content types.

How is this one named? Is this form API?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
If you’re looking for the drag and drop sorting behavior, then you should look at the documentation for
drupal_add_tabledrag.And perhaps this tutorial might help: http://aswapathy.com/d78tu/tabledrag/theme_the_form_doc