In what ways can a person take advantage of another person that they meet in a public place?

That's much too general of a question. A general answer is physically, emotionally or financially. The "how" would obviously vary depending on the people involved. Maybe a better thing for you to remember is "If it seems too good to be true, it probably is."

Teenagers who run away and have no income are vulnerable.  You may just need a place to stay.  You might get addicted to drugs.  Then you may get forced into illegal activities like prostitution, burglary, or selling drugs. 

If you have an income and a place of your own, someone can try to move in, or borrow money, or steal from you, or get you to co-sign for a loan.  Or they can get enough information to apply for credit in your name and run up big bills.

Andy if you're meeting someone from that dating website remember that as long as you're in a public place he can't do anything physically to you. Just don't go anywhere private with him until you're sure he's not some psycho.

Might I suggest Tae Kwon Do lessons. No, I am serious. I don't mean that you should beat hell out of people, though it's definitely a good ability to have if need be. No. If you get a good quality teacher, the martial arts training can instill in you self discipline, self respect and self confidence. Many fine qualities that help you stand up in life and assert yourself in positive ways.

we should be sincere to both ourselves and others.

or it is hard to live with much negative ideas.

better to have a positive attitude.

anyway, you meet the ones of same kinds as u

Anyway you want. And if you pay a little extra. The'll do it with whips and paddles