jQuery UI in Drupal7

From the first sight looks easy but a bit tricky. Ok, we wanna use jQuery UI.
Yes, drupal7 has jquery ui in its core. But:
1) Its in old version. Because of that examples from http://jqueryui.com/ may not work. So we have to use jQuery update.
2) Its not enabled by default.
We need to insert to our code function:

 drupal_add_library('system', 'ui');  

Now we can try jquery ui coding.