Controlling external appliances with a microcontroller by replacing switch with relay
Based on your picture and the wire colors I see, I have a question.  Does the switch light up when the coffee pot is turned ON?  If so, what you have is a SPST (Single Pole Single Throw) switch with built-in indicator.

The blue wire is usually neutral and the brown wire is usually hot or live.  The middle switch terminal is usually the common point of the switch and the indicator.

Because this is a coffee pot, expect some significant current.  The solid-state relay that Some Hardware Guy showed a picture of is a good choice.  Be aware that it probably requires a heatsink.  Pick the heatsink size by assuming that the SSR will drop 1V at whatever current your load consumes.