There are several ways to create a published map with ArcGIS Publisher. The method you choose depends on the type of data used and how the data will be distributed.
Creating a map to share on a network
If you are using ArcSDE or Internet-served data, the published map will work for all ArcReader users that have access to the servers. For file-based data, you must create maps that store the location of the data on the network. If you click a drive letter when you add data from your computer, a local path to the data is stored in the map. To make the map usable on another computer, you need to store the Universal Naming Convention (UNC) path name in the map.
Creating a map to distribute with data
If you plan to distribute data with the map, you need to use relative paths when you create the map. When using relative paths, the map will be able to access the data as long as it stays in the same location relative to the data.
Creating a map with ArcGIS Online data
To publish a map with ArcGIS Online data in ArcMap or ArcGlobe, click File > Add Data > Add Data From ArcGIS Online... 
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Published maps can be uploaded to ArcGIS Online and opened by any ArcReader user. Keep in mind that users of the uploaded published maps will also need access to the map data.
Creating a map with server-based data
When you publish a map composed of server-based data, such as ArcSDE or ArcIMS, the data connection information stored in the map document (.mxd) is also stored in the published map. If the data source requires a password, the ArcReader user will also have to provide a password to view the layer in ArcReader.
You may want to publish password-protected layers for use in ArcReader without giving the password to your ArcReader user. For ArcSDE data, this is done when you make the connection to a spatial database. On the Spatial Database Connection dialog box, there is a Save Name/Password check box. If you check this box during the connection, the password is saved in the map document. This same password will be retained in the published map. If you want the ArcReader user to enter a password to see the ArcSDE data, uncheck Save Name/Password when connecting to the data.