Create the uwawidget-object: $uwawidget = new uwawidget($widgetURL, proxyHtmlUrl);.
Print the needed HTML on your page and you are done: echo $uwawidget->getHtml();.
Custom configuration menu
You can hide the widget-header with the edit-menu if you provide false as thirth parameter of the uwawidget-constructor. You need to provide your own configuration form in this case. You get an array of label/input-html pairs if you call $uwawidget->getPreferencesHtml(). There are two top-arrays: visible for fields you should display as input-fields and hidden for hidden form fields. See example.php for the detailed usage.
If the configuration form is submitted, you can call the uwawidget with the submitted data: $uwawidget->setAndValidatePreferencesData($_POST['uwawidgetdata']). getHtml() automatically submits these values to the widget.
Data entered into the widgets is not shown if the page is reloaded.
If the authetication in a widget is not handled by cookies or a login, there is not much that can be done. It looks like the netvibes dashboard handles the saved datasets and provides these to the widget. No dashboard, no saved data, just default-values.
getMetaData() returns all meta data known for the widget, getMetaDataHtml() prints this information nicely for debugging purposes.