Simple XSLT processor

How an XSLT processor, assuming processor is operating
on a DOM tree for stylesheets (that is the style sheet
instructions are on a DOM tree) operates?

Just searches these stylesheet instructions on the DOM
tree(style sheet tree) and according to the
instructions it modifies the result tree ?
Or there is another way of doing transformation?I mean
the process is different?
Lastly, is there a simple XSLT processor that is
useful for understanding the process?

Thanks in advance.

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