I don't know where you found the idea of Y.DOM.byId
Try
var node = Y.one('#elementID');
or if you want to use classes:
var nodes = Y.all('.className');
For more information on how to get nodes in YUI3, see their documentation
EDIT:
<script>
YUI().use('node', function (Y) {
var node = Y.one('#elementID');
});
</script>