I found my teacher by recommendation. A friend of mine worked with a lady who was really happy with the improvements she found from the lessons.
I never asked for any credentials etc - I just thought I'd see how it went. I was extremely lucky, and my teacher is a total gem. Most of her pupils come to her by word of mouth, and she won't teach anyone that she feels she can't help.
We don't work on folk songs, she teaches using songs & style appropriate to the vocal techniques she is trying to get across to me. It is up to me to then apply that across to my own repertoire (takes a while).
I have a one-hour lesson every fortnight - and practice as often as possible in between the lessons (practice is very important - you need to have the time & place to practice regularly or you are not making best use of the lessons - which are expensive). The first half hour is devoted to warm-ups and exercises - the second half hour is devoted to working on whichever songs we are currently covering. Up til now we have been using show songs (not my fave type of song, but that's irrelevant) - and next we are going to do some classical (which I am really looking forward to).
My teacher also happens to be one of my favourite people. We have a lot of fun, and I absolutely trust that she knows what she is doing with my voice. However she never imposes her preferences on me - and does not consider that the way I used to sing was "wrong", just that I could do much better. She's very patient too - which is a huge help.
So in summary - recommendation is a good way to go - then take some lessons & see how it goes - lessons may not take the form you expect (ie you might learn the techniques in a different style to that which you want to perform in), but you should be able to tell whether you are gaining (but give it a reasonable amount of time, as the improvements start slowish then accelerate)- lessons on their own aren't going to work miracles, you have to practice.... - It really helps if you like and trust your teacher.

KRis