install PHPUnit PEAR extension - see PHPUnit docs for more details
edit main config.php - add $CFG->phpunit_prefix and $CFG->phpunit_dataroot - see config-dist.php for more details
execute php admin/tool/phpunit/cli/util.php --install from dirroot to initialise test database and dataroot
it is necessary to reinitialise the test database manually after every upgrade or installation of new plugins

Test execution

optionally generate phpunit.xml by executing php admin/tool/phpunit/cli/util.php --buildconfig - it collects test cases from all plugins
execute phpunit shell command from dirroot directory
you can also execute a single test phpunit core_phpunit_basic_testcase lib/tests/phpunit_test.php
or all tests in one directory phpunit --configuration phpunit.xml lib/tests/*_test.php
it is possible to create custom configuration files in xml format and use phpunit -c myconfig.xml

How to add more tests?

create tests directory in your plugin if does not already exist
add *_test.php files with custom class that extends basic_testcase or advanced_testcase
execute your new test, for example phpunit core_phpunit_basic_testcase local/mytest/tests/mytest_test.php
optionally build new phpunit.xml by executing php admin/tool/phpunit/cli/util.php --buildconfig and run all tests
core developers have to add all core unit test locations to phpunit.xml.dist

create new test file in xxx/tests/yyy_test.php
copy contents of the old test file
replace extends UnitTestCase with extends basic_testcase
fix setUp, tearDown, asserts, etc.
some old SimpleTest tests can be executed directly - mocking, database operations, assert(), etc. does not work, you may need to add global $CFG; before includes

Why is it necessary to execute the tests from the command line? PHPUnit is designed to be executed from shell, existing Moodle globals and constants would interfere with it.
Why tests subdirectory? It is very unlikely that it will collide with any plugin name because plugin names use singular form.
Why is it necessary to include core and plugin suites in configuration files? PHPUnit does not seem to allow dynamic loading of tests from our dir structure.

add plugin callbacks to data generator
convert remaining tests
delete all simpletests
hide old SimpleTests in UI and delete Functional DB tests
shell script that prepares everything for the first execution
optional support for execution of tests and cli/util.php from web UI (to be implemented via shell execution)