I am curious if it is possible to get a divorce by running it in the newspaper if you do not know where to find your former spouse, and if so how do you go about doing it? Is it expensive?

You don't actually get your divorce though the newspaper, you only do the "legal service" though the newspaper.
It is the most expensive way often to get a divorce.

If you can't find them, and have searched using all the methods the court requires, you have to post it in the legal section of certain newspapers, this can be well over 1000 dollar just for that.

Then you go to court after they are not found.

But it can be done