EDIT Will not display side by side but is stacked - css

Question

I am new to coding HTML/CSS but I have a pretty good grasp so far. I have spent the last few hours trying to get my code side by side but it always remains stacked. My code is
<div class="api" style="float:left;">
<a href="https://play.google.com/store/apps/details?id=com.jrummy.liberty.toolboxpro" target="_blank">
<img src="http://developer.android.com/images/brand/en_generic_rgb_wo_60.png" style="width:50%; border:0" alt="Download ROM Toolbox Pro from Google Play" title="Download ROM Toolbox Pro from Google Play">
</a>
<div>
<div class='appbrain-app'>
<a href='http://www.appbrain.com/app/com.jrummy.liberty.toolboxpro' style='font-size: 11px; color: #555; font-family: Arial, sans-serif;'>
</a>
<script type='text/javascript' language='javascript' src='http://www.appbrain.com/api/api.nocache.js'></script>
</div>
</div>
</div>
And my CSS is,
.api {
margin: 0 auto;
margin-top: 1em;
max-width: 700px;
padding: 1em;
background-color: #e2e2e2;
border: 1px solid #C9C9C9;
box-shadow: 0 0 2px #C9C9C9;
-moz-box-shadow: 0 0 2px #C9C9C9;
-webkit-box-shadow: 0 0 2px #C9C9C9;
border-radius: 3px;
-moz-border-radius: 3px;
-khtml-border-radius: 3px;
-webkit-border-radius: 3px;
display: inline-block;
}
If you tell me what I am missing in order to get the info displayed side by side I would greatly appreciate it. If you have any other code cleanups that you can point out that would be great also but not needed.
EDIT:
Thank you for all your help guys, I have tried both Watson and Pete's answers but sadly they are not working. I took some screenshots of what it is without your code and with your code. You can find them here, https://dl.dropbox.com/u/11217802/sidebyside.png
I have also been able to get it working but I am trying to avoid as much inline styling as possible and I believe that I have pointless tags and way too many <div> for this small project.
<div class="api">
<div>
<td style="vertical-align: middle; text-align: center; background: #e2e2e2; border-top: 0px; ">
<a rel="nofollow" href="https://play.google.com/store/apps/details?id=com.jrummy.liberty.toolboxpro" class="no_ul external" target="_blank">
<img src="http://developer.android.com/images/brand/en_generic_rgb_wo_60.png" style="width:100%; border:0" alt="Download ROM Toolbox Pro from Google Play" title="Download ROM Toolbox Pro from Google Play">
</a>
</td>
</div>
<div style="float: left;">
<div class="appbrain-app">
<a href='http://www.appbrain.com/app/com.jrummy.liberty.toolboxpro' style='font-size: 11px; color: #555; font-family: Arial, sans-serif;'>
</a>
</div>
<script type='text/javascript' language='javascript' src='http://www.appbrain.com/api/api.nocache.js'></script>
</div>
</div>
As far as the CSS, that did not change from what I posted orginally.
Thanks again Grady

Answer 1

try this:
.api a, .api div, .api img {
float: left;
}
and a tip: you should indent your code, so the child nodes are inside the parent nodes, like:
<div>
<a>Example</a>
<img>
<div>
<a>Example</a>
</div>
</div>
sibling nodes (when one tag is not inside another) should be indented the same amount.

Answer 2

looking at your code you have only floated the containing div, all the divs inside it are still block elements, if you want these to be side by side, you can do one of the following:
change them to inline elements .api div {display:inline;}
change them to inline-block elements .api div {display:inline-block;}
float them left .api div {float:left;}
EDIT
Having looked at your edit and tried your code in jsfiddle, the problem is the javascript is creating a lot of extra divs. I have changed your code layout to get things side by side:
http://jsfiddle.net/xFu4Z/1/
html
<div class="api">
<img src="http://developer.android.com/images/brand/en_generic_rgb_wo_60.png" style="width:50%; border:0" alt="Download ROM Toolbox Pro from Google Play" title="Download ROM Toolbox Pro from Google Play" />
</div>
<div class='appbrain-app'>
<a href='http://www.appbrain.com/app/com.jrummy.liberty.toolboxpro' style='font-size: 11px; color: #555; font-family: Arial, sans-serif;'></a>
<script type='text/javascript' language='javascript' src='http://www.appbrain.com/api/api.nocache.js'></script>
</div>
CSS
.api,
.appbrain-app {float:left;}
Please note that you will need to make sure the widths of .api and .appbrain-app added together don't exceed the width of the container they are in - I just noticed that on your original styles you have set a max-width of 700px which means that it is probably going to push the .appbrain-app div down a line

Answer 3

I restructured your markup:
<style>.api {
margin: 0 auto;
margin-top: 1em;
max-width: 700px;
min-width: 300px;
padding: 1em;
background-color: #e2e2e2;
border: 1px solid #C9C9C9;
box-shadow: 0 0 2px #C9C9C9;
-moz-box-shadow: 0 0 2px #C9C9C9;
-webkit-box-shadow: 0 0 2px #C9C9C9;
border-radius: 3px;
-moz-border-radius: 3px;
-khtml-border-radius: 3px;
-webkit-border-radius: 3px;
display: inline-block;
}
.appbrain-app { float: right; width: 48%; border: 1px solid red; }
</style>
<div class="api" style="float:left;">
<div>
<a href="https://play.google.com/store/apps/details?id=com.jrummy.liberty.toolboxpro" target="_blank">
<img src="http://developer.android.com/images/brand/en_generic_rgb_wo_60.png" style="width:50%; border:0" alt="Download ROM Toolbox Pro from Google Play" title="Download ROM Toolbox Pro from Google Play">
</a>
<div class='appbrain-app'>
<a href='http://www.appbrain.com/app/com.jrummy.liberty.toolboxpro' style='font-size: 11px; color: #555; font-family: Arial, sans-serif;'>
</a>
<script type='text/javascript' language='javascript' src='http://www.appbrain.com/api/api.nocache.js'></script>
</div>
</div>
</div>