Northern lights look like a floating ribbon of light. They're very easy to miss if you've never seen them before. The first time I saw them, I thought it was just some car light over the hills. But my parents, who had seen them before, asked me to wait. Within minutes, we could see a ribbon on light floating in the sky, which got thicker as the time passed. Within ten minutes, it was so thick and so low, I felt I could touch it.
As to questing after them: It depends where you are going. I saw them in Iceland, where the government has a very good and accurate website, updated several times a day, that gives you a map of Iceland and the probability of seeing Northern Lights. We always checked that website before leaving, and never had to waste time.
Iceland also has an informal network (other countries might too)- anytime anyone sees the Northen Lights, they let everyone know. In Iceland, all the tourist companies were on this network- as soon as the aurora was spotted, we'd see several buses and cars rushing to the
If you don't want to be disappointed, do your research before leaving, to check if the country you are going to has such support. Iceland is the best country, as Northern Lights can be seen right out of (and sometimes inside) the capital city, which means you don't have to drive hundreds of miles.