Hi Pierre,
A brief test with a new Pages '09 document into which I used Paste and Match style to insert a random text sample (in English, to match the hyphenation dictionary currently in use on my machine) confirms that automatic hyphenation in Pages '09 no longer works under El Capitan. Screen shot below.
Text was inserted, Document Inspector opened and Hyphenation box checked. No hyphenation occurred, even after repeatedly widening the left and right columns to force the text into a narrower column where hyphenation would become more frequent if the feature were working.

As development on Pages '09 ceased when Pages 3 (a new application, not one built on the foundation of what went before) was released, I suspect the "functional and easy process," should hyphenation be the deal breaker, is to use Pages 5 (and lose the many features of Pages '09 that were not included in Pages 3) or some other word processing software which includes the features you need.
Sample text generated by randomtextenerator.com
Regards,
Barry
PS: The article linked in Brendan dv's post is unlikely to be of any use to you—it tells how to turn automatic hyphenation on of off for a document, a selected portion of that document, or a specific word in that document—things I suspect you are already familiar with.
B