It sounds like malbera did it the slick way, but I had only one table to transfer so I did it by hand. I exported my table to an Excel file, saved my excel file as a text file, then imported the text file into a MySql table.
The names of the fields do not matter and you can make allowances for a different amount of fields, but doing it this way is much simpler if you make it match before you export it. The data types need to be compatible, of course.
BTW, you can probably do it directly without any software. I have exported databases from Access to Oracle without any scripting help, just a matter of finding your way through Access's click and point stuff to link them up.