I disagree with the selected answer because depending on what you actually DO, you can be 1 step behind the actually selected value.
If you had some simple delete function then this type of code works fine
var treeview = $("#treeview").data("kendoTreeView");
var selectedNode = treeview.select(),
item = treeview.dataItem(selectedNode);
However, once you start playing with the treeview more you will end up regretting that as I have.
Best practice is to tie to the event handler
e.g.
var treeview = $("#treeview").kendoTreeView({
expanded: true,
select: onSelect,
....
}).data("kendoTreeView");
select function
function onSelect(e) {
var treeview = $("#treeview").data("kendoTreeView");
var item = treeview.dataItem(e.node);
if (item) {
console.log('Selected item: ' + item.whatever + ' | Id = ' + item.Id + ' | Type = ' + item.Type);
var someVariable = item.whatever;
} else{
console.log('nothing selected');
}