There isn't anything you can do during a session other than relax and trust the practitioner until you've selected a practitioner you think you'll be comfortable with and who has appropriate expertise and experience of Reiki.
If you want to learn to better your Reiki experience, try some of the following suggestions:
Bring any songs that you like listening to while you're relaxed.
Before the session, head to the bathroom so you can lay down quietly without being distracted by the need to use the restroom.
If you are very sensitive to touch, it might be helpful to ask the doctor ahead of time which places they intend to touch so that you are aware of what to expect during the session.
Before the consultation begins, inform the doctor of your needs.
Let them know if you have trouble lying down or breathing in those ways, so they can come up with an alternative.
Alternatively, if you've just undergone surgery and are very sensitive in one place, let them know so they don't injure you by handling it. Additionally, whether you are breastfeeding or have bowel issues, you will not be able to lay on your stomach. Let them know, and they'll be able to assist you.
You can become more comfortable as the session progresses. Make sure to change your stance if you feel uncomfortable. If you need some additional assistance, such as a towel or lower back help, please inform the practitioner. After all, this procedure is meant to assist you, and the doctor needs to make sure you have a fun and enjoyable experience.
During Reiki, don't try to push yourself to relax. Reiki is a passive treatment, but you can feel at ease during the session. Allow your mind to wander; pay attention to the sound, your breathing, and the emotions you have throughout the session.
You may also want to read more about Reiki Healing here.