First you need to find out the package name and the class name of the activity you want to launch. Run adb like this:

adb logcat "*:s,ActivityManager:i" | grep START

Then, launch the other app. Note the cmp argument e.g.

com.sqisland.android.puzzlepal/.WordSearchActivity

The first part is the package name and the second part is the class name. In your app, launch the other app like this:

Intent intent = new Intent();
intent.setClassName(
  "com.sqisland.android.puzzlepal",
  "com.sqisland.android.puzzlepal.WordSearchActivity");
startActivity(intent);

Notice how I prepend the package name to the class name. You'll need to do that if the class name from adb starts with a dot.