"I know the ftp username with password" - If the system is set up properly, you should not have access to the database tables from where you are. Assuming for some wierd reason you ftp user has sufficient permissions to access the database then you'd need to use a tool designed to backup a database
You need the following things - you need to know what the database is. This isn't mentioned in the question. You need a piece of software that can dump out the database.
Assuming you're using mysql (and I need to to actually get any further here), you'd use mysqldump to dump the database mysqldump -u mysql_user -p [mysql_password] [database_name] > dumpfilename.sql
then restore it with the command line mysql client - SO covers this well but basically all you're doing is to run the dumped file as the user using it in the mysql client like so mysql -u mysql_user -p [mysql_password]< db_backup.dump
If you are unsure or lacking ANY of these elements, you're best off talking to your DBA or sysadmin. There's also similar questions on DB.SE and SO and I used this site as a basis for my answer (I don't condone the abuse of root accounts tho) and the mysql docs. These are worth looking at.
If you're not using Mysql, the appropriate tool can be found by googling <databasename> dump.
