Access may "work just fine", but it only allows ONE connection at a time. Page requests that are made simultaniously are queued, and visitors have to wait in line for db access. This means that if 2 requests are sent at the same time, one is served, all data requested is retrieved, the connection is closed, and then the second person is served in a similar fashon after all of that. This is the #1 reason Access is slower, and should NEVER be used for ANY type of high-traffic website. SQL databases support and allow simultanious connections and requests for data.
That being said... The differences between the actual SQL INSERT/UPDATE/DELETE code you write are minimal. The most dramatic changes will be in the code to create a new table. Access' TOP will have to be changed to LIMIT for MySQL, and a few other small things. Best thing to do it setup a localhost environment with MySQL, get it to connect to the database, and try out your application. PHP will let you know where the MySQL error are through the 'mysql_error()' function, and you can begin a fix-and-retry process from there.