How does one go about finding a tattoo artist they would like to tattoo them?

I was just wondering. first off do you simply just walk into the shop ask to look at some of the artists work then just leave if you don't like it? It seems quite rude, but on the other hand if you dont like their previous work I wouldnt just have them tattoo me anyways out of politeness. I dont know how to go about finding an artist i like. and what should i look for when looking for an artist? how do i know that they are clean safe and do quality work?