You will need to have at the very least sql server or sql server express installed on the local machine. Then connect to the production server database via SQL Server Management Studio, and create a backup of the production database. .bak file (which may also be zipped). Then copy it to your development server and connect to the SQL Server instance by using SQL Server Management Studio again and then restore the database, by selecting the database that you copied. Open up Kentico and adjust the connection in the web.config.
This is assuming you have a basic install of the system and you aren't using replication, or azure, etc. etc.