This is one of those things that comes with time. It's a balance between being loose and going with the movement of the horse, and maintaining grip/balance.
Most new riders tend to be stiff. I relate it to channeling our inner turtle. When new riders start to get nervous, they turtle up... everything starts to suck up and inward. Legs and knees tuck up closer to body, arms an elbows come in, head/chin down and looking at the horse or ground.
For you to recognize that you are doing it, these are some of the things to watch for- this is when stirrups get dropped, horse breaks gait, or you start to feel like a jockey. Also you will know you are doing it because you get the living daylights bounced out of you. The looser you are, in regards to letting your body hang down and wrap around the horse, the easier it is to move with the horses motion and not bounce. To complicate this, you still grip with your thighs... but not to the point that everything becomes tense.
It's a lot like nuts and bolts - if the rider's nuts, the horse bolts! ~Nicholas Evans