Most new divers wave their hands around. In fact, absence of hand waving is one of the clues to competency that dive leaders look for when we are trying to get a handle on the skill level of a diver whom we have never dived with before--when we see a lot of hand waving, we class a diver as relatively inexperienced. This hand waving is a consequence of feeling a lack of control over one's body position in the water column. When you have this out-of-control feeling, your body will tense up. Once you've learned to use your feet more effectively to steer and use your lungs more effectively to fine tune your buoyancy, you will feel less of a "need" to put your hands to work and you will be able to relax.
Body tension is most often a consequence of psychological stress, so the way to relax is to get past the stress. Leaving aside the fact that individuals vary greatly in the degree of trait anxiety/nervous disposition each possesses, most divers find that experience is the major factor in getting past this anxious phase since everybody is naturally stressed when they're performing new tasks when the skills have not yet become second nature to them. Some people become very stressed if they feel rushed just before entry. Some people feel stressed due to social evaluation anxiety--that is, they worry that they will be judged as deficient by their dive buddies. Environmental factors may play a significant role--cold water, poor visibility, waves/current/surf. Some stress-reduction strategies are straightforward--get ready early if you find that you feel rushed right before a dive--but others, like environmental factors, may require the diver to develop coping strategies, and still others, especially if they are part of your psychological makeup, may take a little more work to conquer. Relaxation skills and visualization/mental rehearsal can help short-circuit rising stress levels pre-dive. Learning and practicing yoga/stomach breathing techniques (breath control exercises) can help since relaxation breathing is a stress preventative. Additionally, the more body-aware you become, the more you will recognize the signs of rising stress levels and then work to get past the stress before it takes over, even under water.