Add an example of using "await" instead of "async with"

This commit adds an example of using "await" instead of "async with"
when opening a new SSHClientConnection. This is useful when you have
code which wants to open a connection and return it without using it
right away. When using "async with", the connection is automatically
closed when the block is exited. Thanks go to Michael Davis for
suggesting this added documentation.

docs/index.rst

@@ -29,7 +29,26 @@ key doesn't match.
       :literal:
       :start-line: 22
 
-This example only uses the output on stdout, but output on stderr is also
+This example shows using the :class:`SSHClientConnection` returned by
+:func:`connect()` as a context manager, so that the connection is
+automatically closed when the end of the code block which opened it is
+reached. However, if you need the connection object to live longer, you
+can use "await" instead of "async with":
+
+   .. code::
+
+     conn = await asyncssh.connect('localhost')
+
+In this case, the application will need to close the connection explicitly
+when done with it, and it is best to also wait for the close to complete.
+This can be done with the following code from inside an async function:
+
+   .. code::
+
+     conn.close()
+     await conn.wait_closed()
+
+Only stdout is referenced this example, but output on stderr is also
 collected as another attribute in the returned :class:`SSHCompletedProcess`
 object.