To add to this, Definitely do some research and be prepared to offer a figure for what you are looking to make at the new job. Always start with the higher end of your ballpark figure though, companies want to hire cheaper if they can. Also, have a cutoff in mind. You can always counter the offer, but be prepared to walk away if it's below your threshold.

I wouldn't give them my current salary if I could help it though. Usually offering an expected salary is enough. If it's not, I'd think twice about working for that company.

If, for whatever reason, you really want the job and they demand to know your current salary, and offering an expected salary isn't enough. I would tell them it's around the lower end of your ballpark figure (assuming that's higher than your current salary). That way, if they want to hire you, they'll at least think they need to beat that.