Here's a list of various simple tutorials to walk through that should provide you with a good base understanding of how to use the Shotgun API and what you can do with it.
.. toctree::
:maxdepth: 1
examples/basic_sg_instance
examples/basic_create_shot
examples/basic_find_shot
examples/basic_update_shot
examples/basic_delete_shot
examples/basic_create_shot_task_template
examples/basic_create_version_link_shot
examples/basic_upload_thumbnail_version
.. toctree::
:maxdepth: 1
examples/ami_handler
examples/ami_version_packager
examples/svn_integration