How to start with MySQL

This is not a trivial request. Since MySQL can handle some pretty heavy duty database tasks, there are a series of steps you need to go through, even for a simple username/password database.

Start off with the MySQL Getting Started Guide Some of it doesn't apply (such as getting and installing), but it will walk you though connecting to MySQL, creating a database and setting up basic permissions.

You'll want to narrow down the question, and will also want to provide a little more detail.

What specific task(s) are you looking to perform?

Can you provide some background on why you're performing the particular task(s)?

MySQL is a common database, though it's been removed from Mac OS X Server 10.7 Lion Server and replaced with PostgreSQL. (You can download and install MySQL onto 10.7 yourself, if you have a requirement for that database.) You may want to stay with a database that Apple will upgrade for you, for instance, rather than one you'll have to download and maintain seperately.

The command-level operations for MySQL are consistent across most installations, so descriptions around creating a database, backing it up, and related tasks are the same. The MySQL documentation is a common starting place for learning about the product, and web content management systems (CMSs) often document the specific command-level operations for each particular CMS package.

As a higher-level GUI interface into MySQL databases on Mac OS X and Mac OS X Server, see the Sequel Pro tool. It's free, and (even better) it's good.

If you're going to be writing programs that store data in it, that leads to additional complexities. (Objective C is built on C, and there are Cocoa frameworks and C native interfaces for most anything around. Other languages will usually have their own frameworks for accessing databases including MySQL, such as php and Python.)

As for your task of storing usernames and passwords on an intranet, that task can involve LDAP or other distributed databases. (This is why I ask for background, above. There can be many reasons for a particular task, and there may be different and variously better alternatives to a particular solution.) If you're looking to perform single-sign-on or related tasks, it's far more common to use LDAP and Kerberos than to roll your own. And tools such as the Apache web server can authenticate against users LDAP, if that's required. (Mac OS X Server includes an LDAP server and Kerberos, and Mac OS X clients can authenticate to this. See the Mac OS X Server Open DIrectory (OD) documentation for related details.)

Here is a general MySQL introduction and here is the mysqldump used for archiving and recovery.

I would not expect to be able to use MAMP and the Mac OS X Server 10.6 MySQL implementation at the same time.