WordPress manage users as non admin

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First off, there is no generic “manage users” ability. There are several individual abilities under that rubric. See http://codex.wordpress.org/Roles_and_Capabilities

Anyway, you have a couple options.

  1. You can add certain capabilities to existing users or
  2. you can create a new custom role with the capabilities you need.

If a brand new role is needed, one can be created using add_role() and add_cap():

$role = add_role('foo_doer', 'Foo Doer');

$role->add_cap('do_foo');

$role->add_cap('do_bar');

If you want to manipulate a user specifically:

// get user by user ID
$user = new WP_User( $id );

// or get user by username
$user = new WP_User( null, $name )

then

// add $cap capability to this role object
$role_object->add_cap( $capability_name );

That’s the basics. A full and elegant rundown is here: http://www.garyc40.com/2010/04/ultimate-guide-to-roles-and-capabilities/