We walked here as there was no convenient metro stop close by. There may be a city bus route...? Afterwards we had access to a hop on / hop off bus that had a stop just across the Tiber.
We arrived here around 4 p.m. as this was a covered stop on our city pass. A bit earlier, a company rep at the Pantheon had called ahead to put us on the list for this site (it hadn't seemed like it required an advance reservation, but it might be worth checking on). We crossed the bridge over the Tiber that leads directly to Castel Sant'Angelo. The statuary on the bridge is worth checking out, and the view of the castle is great for photos as you approach.
We made it to the entrance, but didn't initially see a company rep with an orange umbrella, as expected. However, we turned around and found her off to the side next to the river. We then had to negotiate the ticket-generation process. She apparently wanted to use a couple of messaging apps that none of us had. In the end, she just kept the tickets on her on phone and escorted us in so that she could show / explain to the staff that we should be admitted. It seems like there could be a better way than this, but it worked...
The main draw here turned out to be the views from the top. The architecture is interesting - this began as Hadrian's tomb and originally multiple emperors' ashes were stored here. Then it evolved into a papal fortress and treasury. Most of the artifacts have been removed, so what you are left with is a formidable building without much inside. Don't expect galleries of statues, artwork, etc. There are a few exhibits here and there along your ascent.
The only elevator was for staff only. You first walk most of the way around the circular base and then begin your ascent. You climb a long ramp, which leads to another ramp that traverses the center of the building. You eventually exit out onto a series of terraces and continue climbing stairs. At one point there is a small restaurant / bar with some nice views, but we were not yet hungry. You eventually come out onto a rectangular space close to the top of the castle. From here you have nice views of the city in 3 directions (the 4th is blocked by some remaining structure of the castle). We were fortunate enough to visit a bit before sunset, so the views were enhanced by the late afternoon lighting. It got a bit crowded here, but with a bit of patience it wasn't hard to get to whatever area of the perimeter you wanted for photos.
This is definitely worth a stop, as long as you know what to expect at the outset. It is close to the Vatican, so you may want to combine visiting both on the same day (we did not).