I am interested in translating an English book into my native language.
How can I get permission to translate the book? Would that also include permission to republish the book in the native language or is it another process?
The book's copyright page will identify who owns the copyright to the material. This will typically be the author, or the publisher, or both.
Contact the copyright owner and negotiate to obtain the rights.
If you need more than that, see The Copyright Handbook, which has a chapter on how to obtain copyright permissions.