Online Reference Manual: dev.mysql.com/doc/mysql/en/index.html
MySQL will be installed as a service which will start up with Windows. It is recommended you accept most of the defaults although I did check in the "Include Bin Directory in Windows Path" checkbox (which allows Windows to find executables from the command line if you choose to run it that way occasionally) and you should add a password when given the opportunity -- which you will soon forget so write it down! You may need to configure your firewall to accept the port(usually port 3306).
Grab your favorite MySQL manual and create a database and some tables from the command line. If you're not in love with command line programming give the MySQL Administrator below a try.
The Java-MySQL Connector allows standard Java JDBC commands to access the database. As of December, 2011, the current connector is 5.1.18.
Download and unzip the file linked above. Copy the mysql-connector-java-5.1.14-bin.jar to the following folder in the Java home directory: C:\Program Files\Java\jdk1.7.0_01\jre\lib\ext.
To properly administer a MySQL database you can download or buy the 800+ page manual or you download and use the MySQL Workbench. With the Workbench's GUI interface you can create databases, tables and columns much faster than entering arcane SQL commands in a DOS command box. The WorkBench replaces 3 previous tools: query browser, administrator, and migration toolkit. You can use the Workbench to export databases to other team members on a project.
Find the Workbench tutorial by clicking the Help button or selecting F1.