Note: In this document (and also in the Mesos code base, at least as of Feb 14, 2012), we refer to Mesos Applications as "Frameworks".
See one of the example framework schedulers in MESOS_HOME/src/examples/ to get an idea of what a Mesos framework scheduler and executor in the language of your choice looks like.
You can write a framework scheduler in C, C++, Java/Scala, or Python. Your framework scheduler should inherit from the Scheduler class (see API below). Your scheduler should create a SchedulerDriver (which will mediate communication between your scheduler and the Mesos master) and then call SchedulerDriver.run()