Saving credit card information in MySQL database?
The safest way is to NOT store the credit card information on your system, but let a 3rd party payment provider do it for you.
As mentioned above, do not store credit card information in a database. It's a recipe for trouble. Doing so will make you a very attractive target for hackers and, if they are successful in retrieving them, end your business and potentially ruin your life as well as the lives of those whose credit card numbers are stolen.
Having said that, here are three things to consider:
1) Your best bet is to use a payment processor/payment gateway that offers recurring billing. An example of this is Authorize.Net's Automated Recurring Billing service. Once you set up the subscription they will automatically bill the user every month for you automatically and let you know the results of the transaction. It saves you a ton of work and relieves you of the liability of storing credit card information.
2) If you do store store credit card numbers you must follow PCI guidelines. These guidelines are set by the payment card industry and define what you can and cannot do. It also defines how credit card information must be stored. You will need to encrypt the credit card numbers and you should, but are not required to, encrypt related information (expiration date, etc). You will also be required for ensuring that your web server and network are secure. Failing to meet PCI compliance will result in losing your merchant account and being banned from having a true merchant account forever. That would limit you to using third party processors which are less flexible. Keep in mind that PCI guidelines are a good start but hardly a "how to" when it comes to online security. Your goal would be to exceed the recommendation (by a lot).
3) State and country specific laws supersede PCI compliance. If you suffer a breach and credit card numbers are stolen you risk criminal prosecution. The laws vary from state to state and are constantly in flux as lawmakers are only just beginning to realize how serious of a matter this is.
As far as encryption goes make sure you read up on which encryption algorithms are secure and have not been broken yet. Blowfish is a good start and if you use PHP the mcrypt library is recommended (example).
It's not required that you use a 3rd party payment provider like PayPal, etc. – but you need to be PCI compliant if you are going to store payment card information. Read this article about BC Ferries, who face substantial fines for not keeping up to date with PCI compliance to grasp how serious it is to be PCI compliant.
My current employer is going through PCI compliance – it's not a trivial process, and requires staff for auditing. Enforcement depends on the country and state/province laws – Canada IIRC requires you to be PCI certified by a PCI employed committee, while some states in the US allow for PCI compliance auditing companies to serve in place of the PCI committee.