Steering shaking badly when driving?

My kids and I are on a road trip, which we started yesterday. After we drove about 200 miles on the freeway at fairly high speeds, I noticed a marked vibration or shaking that I can feel through the steering wheel - I noticed this when we exited and reduced speed. I can really feel it now when we are at a low speed but it smooths out when we pick up speed. We are at our destination for a few days and I want to have it looked at, but being in a strange place I don't want someone to take advantage of me, and I don't even know the terminology to tell them what's wrong! Please, in your answer, talk to me like I am a 5 year old because that is about my level of understanding of auto matters. Thanks!