The program "Dumpers" use is warpcopy, it does require some additional hardware, i.e. network cartridge for the C64, a full C64 setup and a diskettedrive (1541-II recommended as it is the easiest to access to clean the head), a PC and network cable.
WarpCopy works as a client server, the C64 being the server and the pc the client, automatic file naming is also an awesome feature of WC.
The reason for using warpcopy is it's efficient way of handling errors.
d64copy with a X(a/e/m)1541 cable or ZoomFloppy can be quite troublesome when encountering errors, even though it does have retries.
I've made a script with parameters set so d64copy would mimic warpcopy. I quickly stopped using it as it didn't satisfy my needs.
Kryoflux and a PC floppy drive can be a good option but isn't as fast as d64copy or warpcopy.
I'm not mentioning nibread (duh, just did) as that would just be pointless unless you're dumping originals.
And of course depending on how the disks were stored, you might need to want to clean the disks.
Translate from Danish, there are some useful links