If the SATA to USB cable works, the hard drive will get a drive letter in File Explorer when you connect it. Then just copy like you copy to or from a USB-stick. You might need to take ownership of some files if access is denied. Google that for your OS.
If it gets no driver letter, the cable doesn't work. Then connect it to a SATA slot on your new computer and it will become an internal drive.
I have a hard drive that I have removed from an old laptop that won't turn on. I am trying to get the data off of this hard drive and onto a working computer. I have a SATA to USB cable but do not know how to do the actual transfer.
Can anyone please help me?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic