I'm starting to use this, and wrote out my notes as I tried it. They are below. An example test case might also be helpful.

The SimpleTest Clone module allows existing Drupal configurations to
be cloned and tested (rather than the default SimpleTest behavior of
building a test site up from install hooks).

This is backport of the cloning functionality of SimpleTest 7.x-2.x.

To install and test:
-------
I. Enable required simpletest module. This should be the simpletest in core; Simpletest contrib (http://drupal.org/project/simpletest) didn't work for me though I didn't work at it. (johnbarclay 1/17/2012).
[drush]
drush en simpletest
[/drush]
-------
II. Run a Simplest of Core as a benchmark (Without Simpletest Clone enabled):
II.A. Run one of the core simpletests to make sure it works without simpletest clone. (e.g. filter tests at: admin/config/development/testing/list).
[drush]
drush test-run FilterAdminTestCase
[/drush]

-------
III. Run same tests with Simpletest Clone.

III.A. Enable Simpltest Clone Module
[drush]
drush dl simpletest_clone
drush en simpletest_clone
[/drush]
III.B. Take that simpletest (e.g. modules/filter/filter.test) file and change the extends from:

class FilterCRUDTestCase extends DrupalWebTestCase {
to
class FilterCRUDTestCase extends SimpleTestCloneTestCase {

III.C. Run the same test as in 2.
[drush]
drush test-run FilterAdminTestCase
[/drush]
-------
IV. Write your own simpletests that implements simpletest clone.

IV.A. Write a simpletest as you normally would, but instead of extending DrupalWebTestCase, extend SimpleTestCloneTestCase. That is:

class MySimpleTest extends SimpleTestCloneTestCase {
...
}