How do you overcome the HTML form nesting limitation?

I would implement this exactly as you described: submit everything to the server and do a simple if/else to check what button was clicked.

And then I would implement a Javascript call tying into the form's onsubmit event which would check before the form was submitted, and only submit the relevant data to the server (possibly through a second form on the page with the ID needed to process the thing as a hidden input, or refresh the page location with the data you need passed as a GET request, or do an Ajax post to the server, or...).

This way the people without Javascript are able to use the form just fine, but the server load is offset because the people who do have Javascript are only submitting the single piece of data needed. Getting yourself focused on only supporting one or the other really limits your options unnecessarily.

Alternatively, if you're working behind a corporate firewall or something and everybody has Javascript disabled, you might want to do two forms and work some CSS magic to make it look like the delete button is part of the first form.

can you have the forms side by side on the page, but not nested. then use CSS to make all the buttons line up pretty?

<form method="post" action="delete_processing_page">
   <input type="hidden" name="id" value="foo" />
   <input type="submit" value="delete" class="css_makes_me_pretty" />
</form>

<form method="post" action="add_edit_processing_page">
   <input type="text" name="foo1"  />
   <input type="text" name="foo2"  />
   <input type="text" name="foo3"  />
   ...
   <input type="submit" value="post/edit" class="css_makes_me_pretty" />
</form>

I know this is an old question, but HTML5 offers a couple new options.

The first is to separate the form from the toolbar in the markup, add another form for the delete action, and associate the buttons in the toolbar with their respective forms using the form attribute.

<form id="saveForm" action="/post/dispatch/save" method="post">
    <input type="text" name="foo" /> <!-- several of those here -->  
</form>
<form id="deleteForm" action="/post/dispatch/delete" method="post">
    <input type="hidden" value="some_id" />
</form>
<div id="toolbar">
    <input type="submit" name="save" value="Save" form="saveForm" />
    <input type="submit" name="delete" value="Delete" form="deleteForm" />
    <a href="/home/index">Cancel</a>
</div>

This option is quite flexible, but the original post also mentioned that it may be necessary to perform different actions with a single form. HTML5 comes to the rescue, again. You can use the formaction attribute on submit buttons, so different buttons in the same form can submit to different URLs. This example just adds a clone method to the toolbar outside the form, but it would work the same nested in the form.

<div id="toolbar">
    <input type="submit" name="clone" value="Clone" form="saveForm"
           formaction="/post/dispatch/clone" />
</div>

http://www.whatwg.org/specs/web-apps/current-work/#attributes-for-form-submission

The advantage of these new features is that they do all this declaratively without JavaScript. The disadvantage is that they are not supported on older browsers, so you'd have to do some polyfilling for older browsers.