Your NAD C315BEE has no "Phono" input. The signal from a phono cartridge is MUCH lower than that from a CD player, tuner, etc. and another stage of amplification is required to bring the signal up to normal level. Some integrated amps already have this, and call it the "Phono" input. You need a separate phono box for moving magnet (MM) cartridge - your turntable plugs in to this, and you need an extra stereo RCA interconnect to run from the phono box's output into any unused input on your NAD. NAD makes well-reviewed phono boxes. Another that comes to mind is the Cambridge 640P. Note that a MC (moving coil) input is not necessary, as your Shure is MM.
PS - You do not sound like an idiot, we all went through this when we first started to listen to vinyl.
