How can I amplify cellphone's vibrator signal to switch my home electricity on or off?
You say you have I would "have a slight knowledge in electronics!

So I recommend not using your phone vibrator to activate something like a solenoid to control mains electricity.

I recommend buying something which does the mains control.

Search for "home electricity control". You will find lots of products which can turn mains power on and off.

Search for "home electricity control wifi" and you will find products which can turn power on and off, and which can be contacted remotely via the internet. 

Once you have control of the mains, and you still want to use your phone, then look at writing an app on that home phone, which talks locally to the mains-controller. If you have a smart phone, e.g. Android, iPhone, etc. then you should be able to write an app relatively easily (there is probably one available already).