mysql package are only client libraries (client-server means that the server may be on one machine and the client on other - but it also may be the same machine), you need mysql-server package to start the server... then you connect to it issuing:
% mysql -h localhost -u root
and you are in...
but to be honest don't learn databases on Access - this is not real relational database. MySQL is quite easy and can do some stuff. but if you really wan't to learn use PostgreSQL - it is the best open source RDBMS comparable to commercial offerings like MS SQL Server or even Oracle. it is not so difficult after all and PostgreSQL has neat features. I suggest you just get some book and dig in...