Great question, To get traffic from SEO it must be done diligently. And the best way to do that is from a well structured article. The key things to remember that will help your pages rank well:

Keyword Headings
Put your most important keywords here. They must be coherent, simple yet descriptive. If your blog allows you to insert H1 headings into your article, do so. Don't cram too much info into keywords though, Search engines are smart and recognize when someone is spamming. Maybe do a bit of research using 'Google Keyword Tool' In Google Adwords and see if your keywords are popular search terms.

Links and Back links
Include links to relevant info when you can, the more credible sources your website links to, the better appeal it has to search engines. Also include back links. Back links are links to a location somewhere that also features a link going directly back to your site, these also give your article good standing.

Duplicate Content
Try not to say anything twice, and if you do use different terminology. But the main focus here is to always write fresh content. If the content of your article has been written word for word somewhere else first how can yours possibly be more credible? Also write often, the more frequent you post articles, the more frequently your site will be "crawled" by bots. If you do this well your listing can only rise.

Be Unique and have the Best Info
This entails just doing what you do and doing it well. It might be difficult to compete with other websites if the topic your discussing is already covered in great detail.

The best position to be in is one of having information that everyone wants but cannot find anywhere else. A good tip for this is finding a specific niche that suits you well to draw in traffic to your general topic.

Hope this helps you get started. For an in depth look at SEO rankings, take a look at the 'Periodic Table of SEO Success Factors' http://searchengineland.com/seotable

Recommend starting with focusing on your audience first. Make sure it's relevant to who you are trying to reach. Pay attention to tone (mirrors the sentiment of your reader) and use simple, friendly and jargon free language.

Structurally these tips may help:

- Page titles (at least 4 words, less than 72 characters) should contain at least one focused keyword/phrase
-Keywords/phrases should appear in the first paragraph but no more than 5.5% density of total words on the page
- Body copy at least 200 words, centered around one or two keywords/phrases
- If images are on the page, add alt-text
- Use no more than one H1 tag
- If the page is more than 300 words, use sub-headlines (h2, h3).
- Include one hyperlink for every 120-150 words of body content (Example: 500 words should have 5 hyperlinks)
If relevant, add interior linking to relevant pages on your website)
- Don’t keyword stuff or spam with linking multiple time to same page

Every page or post should focus on ONE 2-3 word phrase. Use that phrase in the title (ideally first if possible). Also use it as one sub-title as a header 2 <h2> and within the data itself. Shorten the post url to that keyword phrase. (That makes it easier to share and use and useful for SEO.)

Knowing what keyword phrase your content is about helps keep your writing focused. It will result in much clearer posts that your readers will understand better.

These two posts are useful to grasp that concept:
http://growmap.com/building-traffic
http://growmap.com/select-keywords

For how to use header tags properly and complete editorial guidelines for blogging including using images refer to http://www.dirjournal.com/articles/blogging-mistakes/

If you have questions or would like me to explain any of this one-on-one give me a call. I mentor collaborations of bloggers and can connect you with our Blogger Mastermind group.

I would recommend these posts by Neil Patel:

http://www.quicksprout.com/the-advanced-guide-to-seo/
www.quicksprout.com/2013/12/02/how-to-grow-your-blog-to-100000-visits-a-month-in-18-months/

And one more that he links to in the second post.
http://mashable.com/2012/05/08/google-seo-headlines/

I agree with some of the answers that have already been posted. The first step is writing for your audience and making sure you write something people want to read and share. That's why it's called search engine OPTIMIZATION. You're optimizing for computers, not writing for them.

The next step is to optimize, which actually could end up being step one when you conduct keyword research to identify post ideas. If you come up with good post ideas based on sound SEO research and you write great posts for people, then there's a greater likelihood your posts will rank well for SEO. At this point, you just need to make sure you use the keyword phrase in the title and write it in a way that appeals to both people and computers. You can also take a little time to optimize your post and make sure you use the keyword sufficiently in your article without over-using. The Yoast SEO plugin is great for double checking and optimizing after the post is written. Premise by Copyblogger is another tool you can use.

Recap: 1) Write posts that will appeal to people and write for your audience first. 2) Make sure to use the primary keyword in the title and in the post and write the title in a way that will appeal to both readers and Google. 3) Double check with a tool like the Yoast SEO plugin or Premise (although once you get the hang of it you don't have to check as much).

You're absolutely correct to be thinking about SEO, beyond just writing for your audience. I've managed to have some viral posts, but I also get big successes from SEO.

I think these two things are the most important:
1) Have a keyphrase in mind from the beginning, around which to focus the post. Research this, if possible, with the Google Keyword Tool.
2) Monitor Search Analytics to identify opportunities you haven't thought of.

For example, when Google introduced their new logo, I immediately started writing a blog post about it. There was no keyword information available yet, but I figured people would be searching for "new google logo." So, I optimized my post for that.

A few days went by, and I noticed that I wasn't ranking that high for "new google logo." There was lots of competition for this from highly-reputable sites.

BUT, I discovered by looking at Search Analytics, that I was doing pretty well with "google logo font," even though I hadn't optimized for that. Specifically, people were searching for "what font is the new Google logo?"

So, I optimized my post for that (I changed the URL to end with "googles-new-logo-font"), and even fleshed it out a little more to talk more about the font being used in Google's logo. I also changed the title of the post to "what font is the new Google logo?" (notice that I'm still hanging onto hope that I can have a ranking for "google's NEW logo," which may not be the most sound strategy.)

Now, I rank really high for "google logo font," and it is consistently bringing in new email sign-ups.

I've used SEO to entirely fuel 5-figure-a-month passive revenue businesses, and rely in it heavily for building my audience. (I'm not very good at paid traffic, but I'm good at free traffic.) So, if you want to know more, feel free to set up a call.

Research well, gather valuable, intriguing facts and data, give it a new perspective and twist, pour into it your personal style, and voila! You have new great content to publish which in turn will maximize your SEO benefits.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath