If you have an external drive, it's just a hard drive in an enclosure with a USB-to-X board where X is whatever interface is used for the drive (e.g., SATA). You can crack open the case, remove the hard drive, plug in the disk to an adapter like this, and it should be visible in whatever operating system you're using. If it doesn't show up, it's likely something on the disk controller is bad, which is not completely hopeless, but it makes things more complicated.
If it's an old school spinning disk hard drive, and you have bad sectors or the disk is dying, it's possible to use software like Piriform's Recuva to get as much data off the disk as possible before it completely fails.
Absolutely last ditch is a data recovery service which can be pricey, but most of them guarantee a pretty substantial recovery rate depending on the state of the disk itself. If it can be read, and/or the platters are intact, they can get the data off of it.
FWIW the gold standard for long term data storage is still spinning disk. Manufacturing quality is so well-baked that failures are almost unheard of. I have eight 4 TB disks in a NAS that has been running for over 10 years with not a single SMART alert on any of them. If you just want something that's going to store your data long term, get an external hard drive using spinning disk and disconnect it when you don't need it. Put it in a safe, and chances are really good you'll always have access to that data in the future.
Do you know an expert data recovery service?