The CPython core has a raft of machines that do nothing but pull updates from subversion (the code repository) and run the unit tests. You can see the full and somewhat cryptic list of all the boxes and their status on the buildbot webpage. I had to relearn how to read all the output because I had failing tests that only failed on other people's boxen. So here's the HOWTO.
Find your branch
Ten minutes after your checkin reload the buildbot page and find the machines running the branch you checked into. The machines are titled with the codebase being run, currently either "trunk" (aka 2.7), 2.6 (the maintenance branch), 3.0 (another maintenance branch), or 3.x (the py3k trunk). The other words in the name are some combination of hardware, operating system, and compiler.
Open a bunch of tabs
Each vertical column below the name is a time series of builds and statuses with the most recent at the top. The items are either Green (completed, OK), Red (completed, catastrophe), or Yellow (either still running, ambiguous success, or informational). Open a tab by clicking on the "Build NNN" links on all the machines running the branch you care about. Your checkin is listed in the leftmost column so only pick builds than start above (afterwards) that checkin. Then wait an hour or two. [what does the build number mean? I have no idea but I'm guessing the Nth build for that machine]
Check the builds
Most of the builds should have finished so go ahead and reload all the tabs for the individual machines. If the build is still in progress you can tell by the giant header that says "Build In Progress." If it is done you will see a series of little headers and links. Each header is for the different stages: update from svn, run ./configure, recompile the source, and run the test suite. The link titled "stdio" after each of these should be renamed more plainly "view ./configure output," "view test output" etc. This is what you want to see.
Find the output you care about
Search to find the tests and failures that apply to you. Especially on the trunk there may be failures that aren't your fault. Someone elses' checkin might even be causing an abort before your stuff even gets run. If you stuff works, great! If not..
Checkin, rinse, and repeat
Based on the output you may need to make another checkin and let all the buldbots run again. If the failure isn't verbose enough then you will have to checkin some debugging output and wait for them to run again.
.. and that's all there is to it.