There are a number of ways you can achieve this, if you goto the mysql sofware contribution page, there are some VBA functions which produce SQL files from an access database. You can then import these into your MySQL database. (I thouhgt I'll save you the hassle and provide a link:
http://www.mysql.com/portal/software/item-98.html) There are commercial tools which allow this too (here is one:
http://www.realsoftstudio.com/sqlporteraccess.php) In our workplace a popular app was written in access some years ago and due to growth it kept falling over and as a quick fix, I created linked tables so the application thinks its talking to its same old Access table but these are pointing to MySQL behind the scenes.
I hope this helps.