This snippet of code constructs a Handler associated with the main (UI) thread:
Handler handler = new Handler(Looper.getMainLooper());
You can then post stuff for execution in the main (UI) thread like so:
handler.post(runnable_to_call_from_main_thread);
If the handler itself is created from the main (UI) thread the argument can be omitted for brevity:
Handler handler = new Handler();
The Android Dev Guide on processes and threads has more information.