Practicing Pictures

Many of you know that I recently got a new camera, with which I had so much fun on our trip. Thanks to Nicole on A Little Sussy, I have had some ideas on where to start in improving my picture taking skills. I have been practicing my composition and "the rule of thirds". She is also teaching her class about speeding up and slowing down shutter speeds to capture motion, but I don't know how to that. If anyone can give me a tip on that, it would be most appreciated! These are two of my favorite pictures that I took on Saturday (neither of us).