New PC and old PC, having spinning disk (I'm assuming, given the size of data you're talking about), will be connected by 2 cables each. One of these (the larger) is power, the smaller is data.
Old PC should have a spare power connecter floating about for you to use. Unplug the data connector and the disk from new PC, follow the wires on old PC's disk to find where on the board to plug the data in (most desktops have a minimum of 4 SATA data plugs). Do so, and plug in power. Windows should see the disk at boot. Drag and drop.
Direct copy over the SATA bus has less overhead than going via the network, but then network is simpler and doesn't require opening the box. It wouldn't be worth stopping what you're doing for it - zillions of little files and spinning rust are just going to be slow, as the heads spend more time seeking than they do writing - but good to know while 20TB SSDs remain out of the reach of normal people.