Anyone can translate anything without permission. But unless you know for sure that your text has no copyright restrictions (if you can find it in Aozora, for example) you should never attempt to publish your translation without receiving permission/rights to do the English translation. Please note that in this day and age, making your translation widely available by putting it up on a blog or in an institutional repository (like ScholarWorks) can be seen as "publishing" so make sure that you have your permission.
One of the best places to find out about the process is to read the text:
Practical Guide to Publishing in Japan
