Re: retina clinic, if you'll be working with someone for a long time, you can ask if they want to teach you how to set up their tray. I used to set up my attending's injection trays as a medical student...I would draw everything up, I would put the drops in pts and get them all ready for their injection. That being said, I don't think this is something that should be expected unless you're told or asked to it. My attending taught me exactly what to do and how to do it. Medicine is an apprenticeship and I'm glad he let me be involved.
To answer your question, every situation is different. For example, if you're at a prestigious oculoplastics private practice, don't try to be super proactive necessarily. Be a gentleman/lady and try to enhance the image of the practice for your attending by looking sharp and being kind to pts. Be ready to answer their advanced questions when they pimp you. In busy resident clinics it's completely different. Try to help in clinic as much as much as you can. The more you know the more helpful you can be. You can meet pts and document the HPI, take VAs, test pupils, confrontational VF, autorefract, try to work the pt up as much as you can. Ask if they want you to document your external/anterior chamber exam. Ask if you can put drops in. I learned how to do OCTs and help when things got backed up. Take a stab with the phoropter. Eventually you learn to do things.
Agree with the OR advice as above.