This would be my solution to the problem if you want to make edits on the back-end(Admin area) in the site at any time. If you want a static menu just insert step 1 where you needed it and skip the rest. Hope it helps!
Your CODE will look similar to this:
Step 1) Create menu and insert images in images folder within your child theme
<li><a href="https://facebook.com/profileURL" target="_blank"><img src="/wp-content/themes/ThemeNameGoesHere/images/icon/facebook.png"></a></li>
<li><a href="https://plus.google.com/profileURL" target="_blank"><img src="/wp-content/themes/ThemeNameGoesHere/images/icon/google-plus.png"></a></li>
<li><a href="https://twitter.com/profileURL" target="_blank"><img src="/wp-content/themes/ThemeNameGoesHere/images/icon/twitter.png"></a></li>
Step 2) Download "Widgets On Pages" plug in or an equivalent to it. Install and go to your Widgets on pages settings. Located in Settings > Widgets on Pages". Insert the name you want to, i will use "social-section". Go to the "Appearance > widgets" section and add a text widget in the our newly created widget(social-section). We will use this to change the menu on the fly and not have a static menu in our themes php files every time we need to add a social network.
Step 3) Open the file of where you want the menu to go. This can vary from theme to theme to theme. A developer friendly theme will provide hooks for the theme. . My example will use a my parents themes hook to insert the menu we create in step 1 in the desired location. If your theme doesn't have predefined hooks you can look in the wordpress codex for the default wp hooks.
Step 4) Using the child themes functions.php we will create a simple function that will call our widget on pages(social-section)that we created in step 2.
//Custom function that will add our menu when called
echo do_shortcode('[widgets_on_pages id="social-section"]')
//this will run our widget which will contain our social-links UL
//first parameter will be your hook and the second is the function you want to insert
Step 5) Save/Upload and edit the css to your linking. This is a little long but its a solution that you can edit in the backend. If you have any questions for this method please feel free to contact me.