In a way, the question you're asking is off target.
When most people ask "How do I do SEO"? or some variant thereof, what they're really asking is "How do I get found by people through organic search?".
SEO is a critical piece of the puzzle, but in an of itself is not enough. SEO alone with NEVER get you ranked (maybe not never, but you get the idea).
Yes your WordPress site has to be setup right from an SEO perspective. This includes things people don't ordinarily think of as setup, such as your website tag line and category names (assuming you've set your permalinks "right").
Yes your blog posts need to be properly formatted for SEO (which is more than "just" using a good SEO plugin. I agree with the lady who recommended NOT using Yoast - it's a good plugin but it shifts some people's focus from where it needs to be to checking too many SEO technical details, some of which matter very very very little.
So what does it take to be found today via organic search? Publishing!
You don't need an SEO expert per se, you need a journalist/marketer who knows how to properly format posts for good SEO.
I say "journalist/marketer" because what we call Inbound Marketing and/or Content Marketing is generally assigned to marketing, and many people fail because they fail recognize that Content Marketing looks A LOT like journalism.
You need someone who generates articles ideas, writes posts, schedules them, and treats your blog website as an online magazine catering to your desired audience, where the only advertiser in your online magazine is you.
SEO is no longer enough and hasn't been for a few years.
"Publish or perish" is no longer just for academia.
It's for marketing and lead generation too.