I was surprised at how little information I found on making use of Django's permission system. Here are some quick notes on one way to use it:

Groups are groups of users. For example, you could define a group of users who have premium accounts, or have been verified in some way, or are somehow special:

from django.contrib.auth.models import Group, Permission
special_users = Group(name='Special Users')
special_users.save()
really_special_users = Group(name='Super Special Users')
really_special_users.save()

Now you have two groups defined and can define permissions for them. Django associates permissions with models (note: not model instances, but models). You'll need to select a model to apply the permissions to, and do a small dance with "ContentType" to find that model's content type:

from django.contrib.contenttypes.models import ContentType
somemodel_ct = ContentType.objects.get(app_label='myapp', model='somemodel')

can_view = Permission(name='Can View', codename='can_view_something',
                       content_type=somemodel_ct)
can_view.save()

can_modify = Permission(name='Can Modify', codename='can_modify_something',
                       content_type=somemodel_ct)
can_modify.save()

You've now defined two permissions and can associate them with your Groups:

special_users.permissions.add(can_view)
really_special_users.permissions = [can_view, can_modify]

Our groups and their associated permissions are ready to go. Now we just have to associate these permissions with users:

jack=User.objects.get(email='[[email protected]](/web/20120325165629/http://cloudflare.com/email-protection.html)')
jack.groups.add(special_users)

jill=User.objects.get(email='[[email protected]](/web/20120325165629/http://cloudflare.com/email-protection.html)')
jill.groups.add(really_special_users)

We're all done. Now we can check the users' permissions:

>>> jack.has_perm('myapp.can_view_something')
True
>>> jack.has_perm('myapp.can_modify_something')
False

>>> jill.has_perm('myapp.can_view_something')
True
>>> jill.has_perm('myapp.can_modify_something')
True

And to use it in your templates:

{% if perms.myapp.can_view_something %}
Here is something for you to see.
{% else %}
Can't show you!
{% endif %}