It's not overly complicated. Depending on what components you have and what case you're moving them from and to. You unplug everything and move it to the new case. Say you have a standard build with mobo, cpu/cooler, gpu, ssd, hdd etc. I would start by turning off the pc and unplugging the power to the back of the power supply. Remove the power cable from the graphics card, removed the retaining screw(s) at the i/o panel (where the monitor plugs in at and don't forget to unplug the monitor). Pull the gpu out and set it aside. Unplug the data and power cables from the hdd/ssd and remove them from the drive trays or mounts. Unplug the sata cables from the motherboard and set the cables aside. Remove the cpu cooler from the cpu and unplug it from the fan header on the mobo.
If you can't access the back of the cooler (if needed), you may be able to leave it installed and be careful moving the motherboard with the cpu cooler attached especially if it's a larger aftermarket air cooler. If it's an aio water cooler, the radiator will have to be unscrewed from the case and the fan(s) unplugged from the motherboard. You can leave the ram intact usually.
Unplug the cpu power cable and motherboard main power and any fans plugged into the motherboard along with the case front panel ports/pwr connections (usually along the lower side of the motherboard. Unscrew all the screws holding the motherboard in and lift it out making sure nothing is plugged into the back on the io plane, mouse, keyboard, usb, audio - everything needs unplugged.
Depending on the case, you may have to route the cables through the back of the motherboard tray and out through grommets or holes in the motherboard tray. Once the power supply is completely detached from all components, unscrew it from the case and remove it. Go back through everything you did in reverse order and reinstall in the new case. If something seems 'stuck' don't force it and try to sort out why it's stuck. If it's bumping against part of the case you may have to wiggle it. Make sure there's no wires/cables still attached keeping a part from coming out. Better to go slow and steady if unsure rather than force anything and cause damage by yanking a cable out and bending pins or snapping/stressing connection points.