Hi,

You can achieve this with the help of bootstarp platform.

Please find the link of bootstrap:

http://getbootstrap.com/getting-started/

Please see the code below for customize the dropdown:

<div class="dropdown">
  <button class="btn btn-default dropdown-toggle" type="button" id="dropdownMenu1" data-toggle="dropdown">
    Dropdown
    <span class="caret"></span>
  </button>
  <ul class="dropdown-menu" role="menu" aria-labelledby="dropdownMenu1">
    <li role="presentation"><a role="menuitem" tabindex="-1" href="#">Action</a></li>
    <li role="presentation"><a role="menuitem" tabindex="-1" href="#">Another action</a></li>
    <li role="presentation"><a role="menuitem" tabindex="-1" href="#">Something else here</a></li>
    <li role="presentation" class="divider"></li>
    <li role="presentation"><a role="menuitem" tabindex="-1" href="#">Separated link</a></li>
  </ul>
</div>

Once you complete the styling of the dropdown then you have to write javascript on anchor tag for onclick event.

If you are rerending the block in the page then you should call the action function from the javascript function.  Please see the sample code 1 for this.

Sample code 1:
jQuery('.dropdown-menu >li> a').on('click', function () {
                        var val = jQuery(this).text();
                        updateType(val);
                   });

<apex:form>
<apex:actionFunction name="updateType" action="{!updateType}" rerender="postWrapper" >
                    <apex:param name="param" assignTo="{!selectedType}" />
                </apex:actionFunction>
</apex:form>

If you are refershing the whole page after click on the anchor tag then you have to do post request form the javascript function. Please
see the sample code 2 for this:

Sample Code 2:
jQuery('.dropdown-menu >li> a').on('click', function () {
                        var val = jQuery(this).text();
                        location.href = "{!$Page.testPage}?selectedType="+val;
                   });

Let us know if you have any queries.

Please don't forget to Mark this as best answer if it resolves your issue.

Regards,
Grazitti Team
Web: www.grazitti.com