How can I find out a list of available $string values for user_access($string) function?
As @Berdir said, the easiest way to see which permissions are available is to go to the permissions admin/people/permissions in Drupal 7.

The problem I kept running into is that I could never figure out what string I needed to supply as an 'access argument' to actually make use of the permission.  Well, here is how you find the string name for the permissions you want to use (This example uses Google Chrome.)

Step one. Go to admin/people/permissions find the permission you would like to use and right click on a check box to the right of the permission you would like to use.  Select 'Inspect Element' or just go look at the source. 



Next look for the value of the check box and note the value. (In this case the string is 'create coupon content')



This is the string you need to supply as an access argument in hook_menu()

Example Code: (non-relevant items removed, don't forget title, callback, etc. in hook_menu())

function fsrsys_menu() {
    $items = array();
    $items['my-custom-url'] = array(
        'access callback' =&gt; 'user_access',
        'access arguments' =&gt; array('create coupon content'),
    );
    return $items;
}