In very short, the functionality you need are:
Use the Javascript function dynajax.request('respfile: x; resultloc: y; paramloc: z;')
The attributes:
<div id="params">
    <input type="text" name="mydata" />
    <input type="button" value="Submit" 
          onclick="dynajax.request('respfile: myresp.php; resultloc: result; paramloc: params;')" />
</div>
<div id="result">
</div>