I have just installed Windows virtual machine, but it prompts for the activation key every time it starts.
Windows virtual machine has not been activated yet.
Parallels Desktop allows you to have your Windows activation key entered at the moment of the virtual machine's creation. Please refer to Step 5: Enter your Windows product key in KB 113879 to perform Windows express installation.
If you skip express installation step, you will need to activate Windows and install Parallels Tools manually afterwards.
At this point Windows activation procedure will be the same as on the real PC.
NOTE: If you have a BootCamp based virtual machine, please refer to KB 9703.