If your PC PSU has a hard power switch on the back of the power supply, turn that OFF, wait 2 mintues, and then
ground yourself and add / remove hardware as you like.
If your PC PSU has no such hard power switch on the PSU rear itself then you MUST NOT add / remove any cards from the system. You could CAREFULLY add/remove internal SATA drives or fans or such but NEVER connect/disconnect anything relating to an expansion card, do not pull power connectors off the motherboard, don't touch the motherboard, definitely don't remove the motherboard / CPU heatsink / CPU / memory etc. Basically SATA drives and fans are the main things you could even CAREFULLY change safely and then only if you basically touch / disrupt nothing else.
Why? When the PC is turned off and shut down in the normal way, the PSU is STILL RUNNING and the motherboard STILL HAS POWER! It is called standby power and it goes through the motherboard and to all your add in cards. It is not designed to be worked on while this power supply is present!
SATA drives and USB devices and add-in fans aren't connected through this standby power so you could carefully change those.
Now if you just put your PC to SLEEP / HIBERNATE / STANDBY you should change NOTHING AT ALL even if the thing is unplugged or hard switched off -- why -- well because the OS is still "running" in a frozen state that it will recover from and it is not designed to see radical changes in devices while it is in operation or while it is frozen in sleep / hibernate.