As said, if what broke was the hard drive then you may need some recovery work to get the files. Unless all that happened was the OS got messed up and it stopped booting, and then the files may be okay, just it doesn’t boot. If all this is the case, you could have got the old computer working with a reinstall.
If not the hard drive then yes, just plug it into new computer, copy files off with Explorer.
You can do a clone but that will copy the whole operating system and everything, which you may or may not want and you’d need a spare disc to clone it onto. You wouldn’t want to clone it onto the new computer’s hard disc as the OS will be wrong for the computer. Wrong version perhaps, almost certainly the wrong drivers. You just want the data by the sounds of it.