There are a number of different devices that you can use here but the best / most stable are the Tp-Link Smart Plugs.
I use these plugs to control 2 lamps in the living room and even to control the Christmas tree lights!
All I say is “Echo, Turn on Coffee Table Lamp” and the lamp comes on.
This plug just plugs into the socket and so can be used for a variety of things e.g. an electric blanket, meaning you can turn it on from anywhere in your house or even set it up on a schedule to turn on and then off at a certain time.
Setup is easily done via the Kasa app that is then linked to the Amazon Alexa account.
Check out the videos below to see it in action and also how to set them up.