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However - you will need access to some information. Specifically you will need three things:
- database userid
- database password
This information has to come from your webhost - contact them and ask them for it.
Then somewhere in the configuration files for your forum program there will be a text file you'll need to edit. Inside that text file will be a spot to type in the specifics for those three items.
That's all you should need to know about mysql for your forum.
In terms of backing up your mysql database, phpmyadmin is a good choice. Another one is to just use mysqldump. You need to log on to your webserver account (a program called 'putty' will let you do this) and issue the following command:
mysqldump -u yourmysqlusername -p yourdatabasename -a -B>databasebackup.txt
That will dump your mysql database out to a text file with everything needed to do a full restore. Fine for smaller backups, you'll need something better if you have a large forum.
If you ever needed to restore it, you could issue the following command:
mysql -u yourmysqlusername - <databasebackup.txt
I don't think you need to be concerned with anything else to do with mysql.