How to support anonymity on a website?

I'm making a website (using PHP, JavaScript and MySQL) with a voting system which allows people to vote anonymously but just only once.

It means that my system have to know who voted (because I have to check if the user already voted or not)but I didn't want to store the user name or the user's IP address in the database (ruin the anonymity). I don't know how to get started, I need some guidelines; what should I look for?

Solution

Your worst problem is how to make sure your users only vote once, but that's not the point of the question: you are asking how to ensure anonimity

That is rather easy: treat the whatever you use for single-voting as a password, and hash it. So lets say for argument's sake you are using the IP. I'm aware of the problems with that, but lets assume this is your choice.

User votes
You hash the IP and save it.
You can even go as far as saving it in a different location. No need to even save what hash voted which option.
User votes again -> IP-hash is allready in database.
To not give away if someone has already voted, don't reply " you have already voted ", but just don't save the vote. This way there is no way to even know if there was a vote from this machine

Mind you, this is about anonimity, not about how to ensure single-voting.