It is not that difficult. You can get away simply removing the expansion cards (PCI and PCIE-E), unplugging all the cable and leaving the CPU cooler on if you lift when the computer is flat. (if the cooler is enormous and puts pressure by its weight, then remove it and reinstall it when you install in the new case to avoid bending or damaging the motherboard)
Then remove all the screws on your motherboard and leave it on the table. Get the rest of the components out, without the screws as the new cases comes with screws.
Install the I/O backplate of your motherbord first on the new case, you'll thank me later
Make sure the spacers are installed on the motherboard tray of the new case after that, and reverse process. PSU is usually one of the last component to install.
Hope that clears it up a bit