What is the simple subject and simple predicate of the sentence, Mr.Jones is a piano teacher?

The simple subject in this sentence is "Mr. Jones," and
the simple predicate is "is."

Most sentences consist of far
more than a simple subject and a simple predicate, of course, including your example. 
However, no matter what words are included in a sentence, the simple subject can be
identified by asking what or who in the sentence is doing or being. The simple predicate
in a sentence is the verb that shows the action or state of being.  Here is another
example for you:

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Mrs. Smith, who teaches English at the local high
school, donates her old books to the school library, which has increased the library's
collection by hundreds of
books.

Now, in spite of all
the words in that sentence, we can see that "Mrs. Smith" is the person in the sentence
who is doing something.  And we can see that what she is doing is "donating."  So, those
are the simple subject and simple predicate in that example.