Be yourself, let them know you are anxious or nervous- but desire to give their loved one the best care you would want for your family member.
Ask them if they have any special requests. Get them to tell you about the patient, and always explain audibly everything to the patient your taking care of- even if they seem unresponsive.
I know it's a hospice patient, so getting their expectations on your care(which can vary depending on activity level) will be crucial. As for hospice patients, conventional ADL care and turning may be different. Provide good oral care, and if it's a male you can shave his face, if that's what he did, and keep hair presentable. You probably know all this- but showing them you care- and going the extra mile early will set up a rapport between you and the family.
So much care depends on ambulatory status vs. bed bound unresponsive, progression of disease, and present mental status. You will do fine!
Congrats on your first Post in Healthcare!!