Where can I read the debug output of test classes

When you run your test class the debug log does show the logs of even your test execution.

You have to find the user that started the test in question. The user can be found by going to Setup > Develop > Apex Test Execution and inspecting the Test run to find the email of the user.

The line will look like this:

Test run: yyyy-mm-dd hh:MM:ss, [email protected] (n class[es])

Then at Setup > Monitoring > Debug Logs add the user who has the [email protected] email to Monitored Users.

Log 
27.0 APEX_CODE,DEBUG;APEX_PROFILING,INFO;CALLOUT,INFO;DB,INFO;SYSTEM,DEBUG;VALIDATION,INFO;VISmmUALFORCE,INFO;WORKFLOW,INFO
 07:54:37.375 (2375302000)|EXECUTION_STARTED
 07:54:37.375 (2375362000)|CODE_UNIT_STARTED|     [EXTERNAL]|01p90000002IZE6|TestClassName.testMethodName
  07:54:37.376 (2376542000)|METHOD_ENTRY|   [2]|01p90000002IZE6|TestClassName.TestClassName()
 07:54:37.376 (2376557000)|METHOD_EXIT|[2]|TestClassName
 07:54:37.376 (2376695000)|SYSTEM_METHOD_ENTRY|[4]|System.debug(ANY)
  07:54:37.376 (2376721000)|USER_DEBUG|[4]|DEBUG|My debug statement
  07:54:37.376 (2376731000)|SYSTEM_METHOD_EXIT|[4]|System.debug(ANY)
  07:54:37.376 (2376752000)|SYSTEM_METHOD_ENTRY|[5]|System.assertEquals(ANY, ANY)
  07:54:37.376 (2376776000)|SYSTEM_METHOD_EXIT|[5]|System.assertEquals(ANY, ANY)
   07:54:35.608 (2376798000)|CUMULATIVE_LIMIT_USAGE
   07:54:35.608|LIMIT_USAGE_FOR_NS|(default)|
   Number of SOQL queries: 0 out of 100
   Number of query rows: 0 out of 50000
   Number of SOSL queries: 0 out of 20
  Number of DML statements: 0 out of 150
  Number of DML rows: 0 out of 10000
   Number of code statements: 2 out of 200000
  Maximum heap size: 0 out of 6000000
  Number of callouts: 0 out of 10
  Number of Email Invocations: 0 out of 10
  Number of fields describes: 0 out of 100
 Number of record type describes: 0 out of 100
  Number of child relationships describes: 0 out of 100
 Number of picklist describes: 0 out of 100
 Number of future calls: 0 out of 10

07:54:35.608|CUMULATIVE_LIMIT_USAGE_END

07:54:37.376 (2376826000)|CODE_UNIT_FINISHED|TestClassName.testMethodName
07:54:37.376 (2376835000)|EXECUTION_FINISHED

Launch your Devloper Console (Username>Developer Console)

Go to Setup>Developer>Apex Test Execution>Select Tests> pick the testing class you want to see the debug logs from can click run.

Go to your Dev Console. In the logs section you will see the ApexTestHandler operation. Double click that log. Then check 'Debug Only'. You will see your System.debug lines.