If you want to give some users access to different areas of your site, the ability to moderate comments, or create new content, you will need to set more selective permissions. Jeff Traynor has written a great article on Approaches to Access Control, but this tutorial will just focus on Drupal's default only.

Go to Administer > User Management > Roles and create a new role just like in the Configure Your Website tutorial.

Next go to Administer > User Management > Access control (or Permissions)., with the list of permissions and check boxes for each role you have defined; screenshot. Typically, you'll need to visit this page each time you install a new module to grant access to non-super users¹. You can get an idea about what permissions do for each module by looking it up in Core modules.

The following lists describes the function of default module permissions. This list not complete! Please help if you can.

block module

administer blocks

allows use to access the administer blocks page Administer > Site Building > Blocks.

use PHP for block visibility

allows user to enter PHP code between <?php ?> under "Page specific visibility settings"

comment module

access comments

allow user to see and read comments

administer comments

allow user to remove? comments

post comments

allow user to post comments

post comments without approval

what it says

filter module

administer filters

allows user to access the Input formats page where one can define how user-supplied text is processed.
Administer > Site configuration > Input formats

menu module

administer menu

allows use to access the administer menus page Administer > Site Building > Menus.

node module²

access content

Allows the user to view content. This should be enabled for all users, unless you want a private site.

administer content types

Allows the user to edit and add content types at /admin/content/types.

administer nodes

Allows the user to create, edit, and delete nodes of all types. This overrides all the create/edit own/edit options for specific content types below. This also exposes the 'Publishing options' section when editing nodes, allowing users to promote content to the front page, publish and unpublish, make sticky, and create new revisions.

create [TYPE] content

Allows the user to create content of this type. This permission exists for page and story and each additional content type defined on the site. Overridden by the 'administer nodes' permission.

edit own [TYPE] content

Allows the user to edit content of this type that they have created. This permission exists for page and story and each additional content type defined on the site. Overridden by the 'administer nodes' permission.

edit [TYPE] content

Allows the user to edit all content of this type. This permission exists for page and story and each additional content type defined on the site. Overridden by the 'administer nodes' permission.

revert revisions

view revisions

This obviously has to do with the "Log Message" field when creating or editing content. However, checking this doesn't seem to make these revisions display.

system module²

access administration pages

allows users access to the admin path

administer site configuration

allows users to access the site configuration area of the admin panel

select different theme

allows users to change the theme from their profile.

taxonomy module

administer taxonomy

allows use to access the Categories page Administer > Content management > Categories.

user module²

access user profiles

Can see user profiles; users without this set don't see links on user names.

administer access control

Get the admin menu items Access control, Access rules, Roles added to navigation and able to make changes there.

administer users

Get the admin menu item Users -- can list all users, activate accounts, but NOT set roles.

change own username

what it says on the tin

Non Default Modules (at least not in 5.7 6-Feb-08)

path module²

administer url aliases

allows users the ability to administer the url aliases (modify, add, remove)

create url aliases

allows users to create url aliases

¹Jeff Traynor, http://www.jefftraynor.org/node/96 paragraph 2.
²Copied from Access Permissions reference