A very easy to use and fully markup-driven action sheet
<a data-icon="plus" data-role="actionsheet">Open</a>
<div>
<a data-role="button" href="#">Action 1</a>
<a data-role="button" href="#">Action 2</a>
<a data-role="button" href="#">Action 3</a>
<br/>
<!-- This close button is optional. The widget also closes if you click or touch outside of the popup -->
<a data-role="button" data-rel="close" href="#">Cancel</a>
</div>
Also you can use html ids to associate toggle and sheet. This way the sheet must not directly follow the toggle.
<a data-role="actionsheet" data-sheet='sheet0'>Open</a>
.... A lot a lot a lot markup in between ....
<div id='sheet0'>
<h1>This is sheet0 speaking</h1>
</div>
Just like you can change the look of the "Action Sheet" with CSS, you can change the animation via CSS. The default CSS contains two different animations. "actionsheet-open/close-slideup" and actionsheet-open/close-fade. The standard uses "actionsheet-open/close-slideup". If you like the fade animation better change the CSS classes ".ui-actionsheet-animateIn" as also ".ui-actionsheet-animateOut". Change the property"-webkit-animation-name" and "-moz-animation-name" accordingly. Of course you can also use your own animations.
If you are looking for a programmatic javascript approach take a look at this usefull plugin: https://github.com/jtsage/jquery-mobile-simpledialog