Sometimes page owners have it set up so that other pages can't actually do this. In that case you can always log in as yourself and do it that way.
Before using this method you should suss out if the page owner will accept your posts or not. You can get an idea about whether this will be the case by checking if other people have already done so.
Also, the character of the page owner comes across in its content. Some are clearly heavily into branding and it's all about them. In this kind of page the only contributions you see in this section are comments about how wonderful the page is, and how much the commenter is looking forward to the next webinar, etc. You don't want to be posting blog links to pages like this, because they will probably be deleted.
It's usually not worth posting links on pages with absolutely no monitoring either. They'll be overrun with spam and no one will click on your posts.
There are pages that are halfway between these two extremes, however. They are the ones to go for.
Obviously you don't want to only ever submit your own, irrelevant, blog posts. That's spamming. You have to include only those posts that are relevant to the subject matter of the page. If you do that on popular pages you will get occasional clicks coming through. You'll also be getting some exposure for your own Facebook page. The other fans of the pages you're doing this on will see your page name, after all. That's why it's important to only share quality, relevant blog posts. And it always helps if you include a little introduction about the post you're sharing, and maybe even why you did so (although it's not absolutely vital).
I've been doing this for a while now and the traffic certainly does come in from this, albeit slowly. Also, I've been getting quite a few likes on those posts from the page owners themselves. This is a good sign because it proves that they don't resent this approach. Nice to know because you don't want to be annoying them.
As well as sharing your own blog posts, you should also include links to those by other people. Doing this shows that you're not only trying get traffic for yourself. Your aim is to contribute useful information to the fans of that page.
You should also write the odd comment on the page's updates, as well as liking them occasionally. The owner will appreciate this and see that you're not just taking advantage of their page. You are engaging with it in a range of ways.