I am sorry for the delayed reply,
There are a few things that are new as a convept in Silverlight, but I am sure that you will quickly find your way around.
Sometimes in our examples we use the Model-View-ViewModel pattern (you can find a lot of examples and explanation for it online) but if you are just starting with Silverlight you may find it wasier to do more things in C# code, more like a WinForms application.
Generally all ContentControls and ItemsControls accept objects as content, which means that you can put anything as the content of the TabItem (or any ItemsControls).
An easy way to achieve what you need is to handle the SelectionChnaged event of the TreeView and create a new TabItem with the header and content (the UserControl) you need and then add it to the Items collection of the TabControl and then selected (set the SelectedItem property).
The close button could be put as an overlay in the top right corner of the TabControl. Then you will need to handle its clicked event and remove the SelectedItem from the items collection.
My example used an ObservableCollection and binding and you can (and should IMO) use this once you are more comfortable with Silverlight / WPF.
Hopefully you will be able to achieve what you need.
the Telerik team