<p>I am using Installshield 2008 Developer Edition and need to run SQL scripts against an existing SQL Server 2005 Express. When I do this without InstallShield, I would have to have some ODBC drivers installed for example. </p>

<p>How does InstallShield do this? Does it include some sort of driver? Or does it depend on preexisting drivers?</p>

If you are having the database installed by Installshield as part of your installation, Installshield has all the information to simply use a connection string like this:
"Driver={SQL Native Client};Server=localhost;Database=newdatabase;Uid=proguser;Pwd=progpass;"
There is no need to create an ODBC connection to use a connection string like this, and Installshield makes the SQL Native Client a prerequisite  for SQL 2005 connected databases, so it is assured of having the correct driver available.