There are a bunch of steps to consider, and your security will end up being as good as you want it to be. I will give you this article:
Securing MySQL: step-by-step
It is an incredible resource and describes a bunch of things you can do to secure your MySQL server. I hate to respond with a link, but securing something like this is really a task that can't be prescribed in the same manner for everybody, I don't believe, it must be done to our liking with as much knowledge about the process as you would like to know.
Good luck and HTH.