I would follow @Phrancis answer regarding your header and SEO. As far as the rest of the markup, I would do things a little differently and I'll cite some articles to explain why:
The body header section looks fine to me, nothing out of the ordinary. The Content is where I would change somethings. For example:
<header>
<h2>About Me</h2>
</header>
This <header> isn't necessarily needed. The <h2> tag already tells the browser that this is the header of our article since it's the first one found under the <article> tag. I would also change it to an <h1> tag, since it's the at the beginning of the article.
From HTML5 Doctors Common HTML5 Mistakes
If your <header> element only contains a single heading element, leave out the <header>. The <article> ensures that the heading will be shown in the document outline, and because the <header> doesn’t contain multiple elements (as the definition describes), why write code when you don’t need to?
And since our <article> tag starts a new document outline, we can define a second Header 1 tag to define its title ( The first being DEdesigns ). Here's a good article from Web Design Tuts+ explaining why this is O.K. to use in HTML5 and why we are so used to old practices. TL;DR of the article: The body starts a general document outline but each article also starts a new document outline and needs its specific heading title ( h1 through h6 ).
Another issue I see is that <section> is not necessary as there isn't multiple in your document outline ( in your article ). Semantically you can just add the paragraph after the heading which will automatically define the content of your article, no section necessary. If your page was a wikipedia article, then there would be a reason to use sections but since it likely is just normal page content the section is not necessary here.
In your Gallery I believe if these describe the figures they should be wrapped in <figcaption> to be properly parsed.
It seems odd to have all these <h1> tags but since HTML5 articles defines a new document layout it should be done like this so that each article has the same emphasis on the title.
This is option 1:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>DEdesigns</title>
<script scr="html5shiv.js"></script> <!-- allows html 5 styling -->
<link rel="stylesheet" href="style.css">
</head>
<body>
<div id="container">
<header>
<h1>DEdesigns</h1>
<nav>
<ul>
<li><a href="#">Home</a></li>
<li><a href="#">About</a></li>
<li><a href="#">Services</a></li>
<li><a href="#">Contact</a></li>
</ul>
</nav>
</header> <!-- end header -->
<article id="about-me">
<h1>About Me</h1>
<p>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged</p>
<aside>
<figure>
<img src="#" alt="#" width="#" height="#">
</figure>
</aside>
</article> <!-- end #about-me -->
<article id="gallery">
<h1>My Work</h1>
<div id="gallery-conatiner">
<figure>
<img src="#" alt="#" width="#" height="#">
<figcaption>
rem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500
</figcaption>
</figure>
<!-- ends first row -->
<figure>
<figcaption>
rem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500
</figcaption>
<img src="#" alt="#" width="#" height="#">
</figure>
<!-- ends second row -->
<figure>
<img src="#" alt="#" width="#" height="#">
<figcaption>
rem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500
</figcaption>
</figure>
<!-- ends third row -->
</div>
</article> <!-- end #gallery -->
<article id="services">
<h1>Services</h1>
<ol>
<li>one</li>
<li>two</li>
<li>three</li>
</ol>
</article> <!-- end #services -->
<article id="contact-me">
<h1>Contact Me</h1>
<p>some contact me stuff goes here</p>
</article> <!-- end #contact-me -->
<footer>
<p>This is my footer</p>
<small>Copyright in Small</small>
</footer>
</div> <!-- end #container -->
</body>
</html>
Another way you could look at it since this is a flat design is wrap EVERYTHING in a <main> and <article> tag. The <header> would be inside your article since it defines navigation ( think back to wikipedia ), then each <article> tag would turn into a <section> or your article. So that semantically it would look like this:
- DEdesigns
- About Me
- My Work
- My Services
- Contact
This is assuming of course that the <nav> links are Jump Links or will move down the page to the corresponding section whenever click Versus loading a new page.
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>DEdesigns</title>
<script scr="html5shiv.js"></script> <!-- allows html 5 styling -->
<link rel="stylesheet" href="style.css">
</head>
<body>
<main id="container">
<article>
<header>
<h1>DEdesigns</h1>
<nav>
<ul>
<li><a href="#">Home</a></li>
<li><a href="#">About</a></li>
<li><a href="#">Services</a></li>
<li><a href="#">Contact</a></li>
</ul>
</nav>
</header> <!-- end header -->
<section id="about-me">
<h2>About Me</h2>
<p>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged</p>
<aside>
<figure>
<img src="#" alt="#" width="#" height="#">
</figure>
</aside>
</section> <!-- end #about-me -->
<section id="gallery">
<h2>My Work</h2>
<div id="gallery-conatiner">
<figure>
<img src="#" alt="#" width="#" height="#">
<figcaption>
rem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500
</figcaption>
</figure>
<!-- ends first row -->
<figure>
<figcaption>
rem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500
</figcaption>
<img src="#" alt="#" width="#" height="#">
</figure>
<!-- ends second row -->
<figure>
<img src="#" alt="#" width="#" height="#">
<figcaption>
rem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500
</figcaption>
</figure>
<!-- ends third row -->
</div>
</section> <!-- end #gallery -->
<section id="services">
<h2>Services</h2>
<ol>
<li>one</li>
<li>two</li>
<li>three</li>
</ol>
</section> <!-- end #services -->
<section id="contact-me">
<h2>Contact Me</h2>
<p>some contact me stuff goes here</p>
</section> <!-- end #contact-me -->
<footer>
<p>This is my footer</p>
<small>Copyright in Small</small>
</footer>
</article>
</main> <!-- end #container -->
</body>
</html>
Feel free to ask me any questions and I'll try to clarify as best I can or give better reasoning on why I did A over B.
style.csscode as well? This will make the review more useful. Thank you! \$\endgroup\$