Is it free to meet someone and talk to them on Yahoo Personals?

No. You can sign up for an account and send premade messages to other people but thats it. If you ever want to contact a person and chat with them by email or other, you will need to set up a paid account. However, you can still be contacted by other paid members, even if you are a free member. You just won't be able to message them back unless they give you their email address on the message.