I worked in outpatient in a subacute SNF type of environment (basically where geriatrics got discharged to from hospital, where they would stay for a few weeks before being discharged to home). My experience was extremely hands-on.
I worked one-on-one with patients several times a week, including transferring them to/from different machines, beds, and wheel chairs. I would take them through different exercises through individualized programs customized by PTs. I'd generally try to increase their exercises over the weeks so they'd ideally progress. I pretty much befriended all of them, and even visited a few later on when I was no longer working there.
This experience was really valuable, and I consider myself really lucky to have been given that much leeway as a rehab aide. I have a grasp as a result on what type of dynamic you can expect with outpatients and their various conditions and personalities, and some of the things to be aware of. I have yet to really get into the troubleshooting aspect of PT, though, and this is the part that I imagine grad school and lab experience will bolster substantially.
Edit: Note the above was employment, not observation/volunteer. For observation/volunteer, in a hospital I helped a bit with ambulation (as many have mentioned) but mostly followed PTs around and stayed out of the way. In a sports outpatient clinic I pretty much just wiped down surfaces and talked a lot with patients and staff.