What do people ask from an astrology reading?
You can literally ask anything. Generally, those who come to astrology are looking for guidance/connection with something much bigger and unbiased than themselves (or another).
Common questions include things such as: What is the purpose of my life here? How will my year go? What are some suggestions to have a better year? Why am I having difficulty in my relationships? How do I make things better for myself? Why do I feel this way about my job, career, friends, spouse, mother etc.? How can I utilize my strengths? Can I know more about (general topic).
What you ask should really just be guided by the questions most important to you. Additionally, your astrologer can clarify exactly what can be seen (by them) and how to approach the topic you're interested in learning about.