Welcome to our forum.
Re: does poly work ... not in every case, but in many cases, yes it does.
Re: what are the pros and cons ... perhaps the biggest drawback is the lack of mainstream support. Other pros and cons largely depend upon the personality that is uniquely you. For instance, is polyamory important to you; do you want it in your life? Is communication a challenge for you? etc.
Re: the best way to get into a poly relationship with another person ... I personally advocate getting to know people as friends first, so that poly gets talked about before it becomes a "hot-button" issue. But for some people, breaking right out into the dating scene and taking it from there is preferable.
Re: the best way to approach a person you'd like to be in a relationship with ... I suppose the direct approach would be best as a rule, e.g., "We are interested in developing a relationship with you, and wonder if the feeling is mutual." But I think you'd want to get to know that person as a friend for awhile before that.
Re: key points to look at before you get into this ... I would spend some time reading the various threads on this site. Probably the top three points are honesty, communication, and compassion. Commit yourself to getting better at all three.
Re: is it better to start with someone you know or start with a new face ... I think that depends on the individuals involved, but often starting with someone you know is a good advantage. Like I said, discussing poly with someone while still in the friendship stage with them creates a kind of "safe place."
Re: what is the best way to talk to her about it ... I'd probably start by just telling her you identify as poly, and what that means to you. Find out what her thoughts are on the matter before investigating any potential mutual attraction or what have you.
Hope some of this helps.
Love means never having to say, "Put down that meat cleaver!"