There are several ways to set up the Workspace Security setting on your workspace. Different kinds of workspaces require different security set ups, so please refer below to find the kind of set up that is best for you. To access the Workspace Security settings, just click "Settings" in the upper right corner of the workspace, and "Workspace Security" on the left hand side.
Private - Personal Use
This kind of security is best if you're using PBworks for your own personal use, and would never want anyone, besides yourself, to have access to the information inside. The only way for anyone to view the contents of your workspace is to log in with your email address and password, which should never be shared.
Private - Group Use
This kind of security works best for small groups, where members are invited when the workspace is first set up, and new members should only be added if the administrators give permission for them.
Publically viewable
This is best for a situation where you want the information to be viewable to the public, but you don't want the public to be able to edit the content. In this security model, there are only a select group of writers and editors on the workspace, but anyone with an internet connection will be able to read the content.
Publically editable
In this security model, anyone can sign up to edit your workspace, and they will be able to edit right away. This is the least secure method, since you're opening up your Workspace to be edited by anyone that wants to sign up for it and has a PBworks account. However, there are safeguards in place to make sure that new users that get added can't do too much damage.
New users that add themselves to a publically editable workspace are added as Writers, so they are able to edit existing pages, create new pages, and upload new files. They are not able to delete any content, or do anything on the workspace that cannot be undone.
Customized Workspace Security 
On free basic workspaces, the only security options available are in the Settings, as described above. These settings deal with Security settings for entry into the workspace, and once a user is granted at least "Reader" access to a workspace (or the workspace is made publically viewable or editable), they will have access to all the content.
With a premium workspace, Administrators are able to set customized security for individual pages and folders, so certain content can be hidden from certain users and shown to other users. If you have a premium workspace (or your workspace is a "Professional Trial"), you have access to these special security features. You can read more about setting page and folder security at the following pages:
This feature has a video tutorial
This feature is new/improved