I would like to start this off by saying I am NOT an SEO expert of any kind. I do however do a decent bit of research and can tell you things you can do on your website to help improve your SEO. First thing is your site needs to be responsive, some people may tell you this is a nice add on (its not an add on) but its required now due mostly in part to googles new ranking algorithm which basically says if there isn’t a mobile version of your site then bye. This is because the use in mobile devices has boomed in the last 5 years. On the subject of mobile, before there was responsive design you would have to create a separate site for mobile users and direct users there if they were viewing from a mobile device. Today, this would be an awful idea. First, its creating more work than necessary and secondly, I don’t think google likes it.
The best thing to do is to have your site built responsively, what this means is you have one site and set of mark-up and the only difference is your styles will update depending on the sizes set in your style sheet. This saves you from having to duplicate content thus saving you time and money.
In addition to making your site mobile friendly you’ll need to make sure your mark-up is optimized the best it can be for bots when they crawl your site. If your first thought is, i’ll add some meta tag keywords then you’re wrong. The days of meta tag keywords are behind us. Unless you have a SEO campaign and some very unique keywords. What is important is to make sure your site is optimized to be shared over social media. These tags are called OG (Open Graph) tags. With these tags you can specify the description of the page (preview content), type of page, and an image associated to the page. This will allow your page to be shared the way you want on social media.
The last important thing for your mark-up is to try and stay within the standards. What I mean by that is there are rules around HTML and how it's to be used. Follow the simple stuff like using alt tags on images, title tags on anchors, only 1 <h1> tag per page, use <em> instead of <i> for italics, and <strong> instead of <bold> these things go a long way and keep your mark-up clean. Also, try using image names that describe the image and not just generic names like image or logo.
Again, I'm no SEO specialist, these are just a few things I do to make my sites as SEO friendly as possible.