In most situations MySQL is stable and easy to diagnose and fix when errors occur. If the following hints do not help then you must contact your host as ultimately they control it's behaviour and keep it performant for you.
By far the most common error especially during new installations. The problem is the script cannot communicate with MySQL, this can be for many reasons and these are the most common:-
5, 6 and 7 can only be fixed by your host. To check 1,2,3 and 4 open your /mysql_config.php file and make sure the settings match those of your database. If none of this makes much sense checkout the videos, particularly How to complete the installation after the files are uploaded.
The full error will look like the following:
You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near [....]
This error will usually happen because of a configuration error. Sometimes when saving the configuration (especially after a cut and paste action) and invalid character causes an error. To diagnose this problem check the last change you made to the configuration, try the previous setting, if that doesn't work make another backup of your /data/config.inc.php and restore the last working backup.
If that fails then report it on the forum not forgetting to supply the following information:-
Your php/mysql client is either not installed or not installed properly. Read this article for more information, however your host should take care of this for you, it may be wiser to contact them first.
User 'xxxxx' has exceeded the 'max_questions' resource (current value: nnnnn)
This error is due to a maximum number of queries set by your host. xxxx is your username and nnnnn the current number of queries per hour they allow. Contact your host and ask them to increase it, if they won't look for a new host.
Most of the time your host will be fixing the following errors for you before you know they have happened. The following is provided if you run your own dedicated server or would like more knowledge on the error before you report to you host.