How do I install CiviCRM on Backdrop?
EDIT: Since this answer, @herb has expanded on this in the Wiki. See "Installing CiviCRM for Backdrop CMS"

There is now an official version of CiviCRM for Backdrop. Once CiviCRM code is placed in /modules, go to 

http://MYWEBSITE.COM/modules/civicrm/install/index.php?civicrm_install_type=backdrop

to install. Note the flag to tell the installer that we're installing for Backdrop otherwise it'll not recognize it.



The code changes to get the installer working for Backdrop is almost done (it's waiting to be tested and merged in https://github.com/civicrm/civicrm-core/pull/8177). You've got three options:


Install manually: run the civicrm.mysql queries on your database (in /modules/civicrm/sql/) and manually build the civicrm.settings.php file (from /modules/civicrm/templates/CRM/common/civicrm.settings.php.template) and put it in your webroot (same level as settings.php).
Apply the patches above to tarball you downloaded (plus apply this patch https://github.com/backdrop/backdrop/commit/93ecec4c081002bfc46fec421b5642d496ca3dac to backdrop. Then navigate to example.com/modules/civicrm/install/index.php?civicrm_install_type=backdrop to run the Backdrop-specific installer.
Or, wait until the next CiviCRM 4.7.x minor release and Backdrop 1.x minor release and it should be working well enough. (Use the same url: example.com/modules/civicrm/install/index.php?civicrm_install_type=backdrop)