I am a historian.
Most important questions are - Where is the diary now? Who does it belong to?
If it's a family record in your possession, possibly the most straightforward thing (albeit time consuming) would be to transcribe it and scan it, if its condition permits, and publish it on a website.
Or if it has some wider significance - the diarist is someone well known, or wrote about important events - you could offer it to a record office as a donation or permanent loan, and they would make it available to researchers.
If it's already in a record office, you'd have to make a transcript for publication.
You don't need to publish the whole thing, though; you could just write about it, including quotations, if you wanted to. There are lots of papers of historical significance in private hands which are used for research but not published.
If the diary is in your possession, or in the hands of another non-expert, please take care that it's stored in suitable conditions.