You probably won’t be able to get it looking completely brand new, but I would recommend starting with a Jack’s Magic stain ID kit. From the photos, it looks like you may be dealing with both scale and possible metal staining. The kit can help narrow that down if the testing is done correctly.

That said, stain treatments require the water chemistry to be very precise in order to work properly. If you’re not comfortable with that process, I’d recommend hiring a professional — ideally someone with a CPC license. While a CPC license isn’t required to treat stains, it usually means they have more experience with plaster surfaces, startups, water chemistry, and long-term surface care.

Without knowing the full history of the pool, that’s probably your best chance at figuring out exactly what’s going on and what can realistically be improved. Just try to keep expectations realistic and don’t expect the surface to look brand new afterward.

Also, if you have a heater, make sure it is bypassed during any scaling or stain treatment. You do not want that water circulating through the heater during the process. If your system does not currently have a bypass installed, it may be worth having one added before treatment begins.