I have installed SQL Express with an instance name of CTHOG and set the login mode for mixed.  I then set a userid of sa with a password of cthog.  I can then use osql to connect to the database (using the cthog password)
c:\
>osql -U sa -S (local)\CTHOG
Password:
1>

I am assuming that since the 1> prompt appears, the connection was established and SQL Express is working.  I am not sure of other SQL Express setting are required...

I then tried to edit the web.config and set the Server=, uid= and pwd= values used above:

  <connectionStrings>
    <!-- Connection String for SQL Server 2005 Express -->
    <add
      name="SiteSqlServer"
      connectionString="Data Source=.\SQLExpress;Integrated Security=True;User Instance=True;AttachDBFilename=|DataDirectory|Database.mdf;"
      providerName="System.Data.SqlClient" />
    <!-- Connection String for SQL Server 2000/2005
    <add
      name="SiteSqlServer"
      connectionString="Server=(local)\CTHOG;Database=DotNetNuke;uid=sa;pwd=cthog;"
      providerName="System.Data.SqlClient" />
   -->
  </connectionStrings>
  <appSettings>
    <!-- Connection String for SQL Server 2005 Express - kept for backwards compatability - legacy modules   -->
    <add key="SiteSqlServer" value="Data Source=.\SQLExpress;Integrated Security=True;User Instance=True;AttachDBFilename=|DataDirectory|Database.mdf;"/>
    <!-- Connection String for SQL Server 2000/2005 - kept for backwards compatability - legacy modules
    <add key="SiteSqlServer" value="Server=(local)\CTHOG;Database=DotNetNuke;uid=sa;pwd=cthog;"/>
    -->

However, when I attempt to connect the first time, I get an error that it could not connect to the database and the 2nd attempt results in an Assembly version not matching a database version.

Any help would be greatly appreciated.  I did only change those fields (Server=, uid= and pwd=) in web.config.  Maybe I should not have used mixed authentication in SQL Express?  Or was I supposed to set some other settings in SQL Express?  Any help would be appreciated!

You have your "Connection String for SQL Server 2000/2005" connections still commented out.

Here is what you should replace it with (changes are in Red) ..

  <connectionStrings>
    <!-- Connection String for SQL Server 2005 Express
    <add
      name="SiteSqlServer"
      connectionString="Data Source=.\SQLExpress;Integrated Security=True;User Instance=True;AttachDBFilename=|DataDirectory|Database.mdf;"
      providerName="System.Data.SqlClient" /> -->
    <!-- Connection String for SQL Server 2000/2005 -->
    <add
      name="SiteSqlServer"
      connectionString="Server=(local)\CTHOG;Database=DotNetNuke;uid=USER;pwd=PASS;"
      providerName="System.Data.SqlClient" />
  </connectionStrings>
  <appSettings>
    <!-- Connection String for SQL Server 2005 Express - kept for backwards compatability - legacy modules
    <add key="SiteSqlServer" value="Data Source=.\SQLExpress;Integrated Security=True;User Instance=True;AttachDBFilename=|DataDirectory|Database.mdf;"/>   -->
    <!-- Connection String for SQL Server 2000/2005 - kept for backwards compatability - legacy modules -->
    <add key="SiteSqlServer" value="Server=(local)\CTHOG;Database=DotNetNuke;uid=USER;pwd=PASS;"/>

Also, mixed authentication is correct, however, you should not use sa acct. Create a login, then a database user, then give the user dbo permissions after adding the user to your DotNetNuke database.

This is all explained in the installation guide, which you can get here.

One last thing .... never paste your uid or pwd here (I changed it to USER & PASS, so you will have to fix it if you paste the above text) .... you never know who might decide to "knock" on your sql back door