Steps for cleaning
Fill the kettle up to half or three quarters level with equal parts of water and white vinegar.
Bring the solution to a boil.
Turn off the kettle and remove its power cord plug from the wall outlet.
Let the vinegar-water mix sit in the kettle for 15-20 minutes. Now, throw the water away and rinse the equipment. You may have to rinse several times to make sure there is no trace of vinegar remaining in the kettle. You shall be amazed to find that you have gotten rid of the chunks of lime scale so easily.
Wipe the inside of the kettle with a clean cloth and leave it to dry completely.
After drying, you can again boil water in the kettle and discard it to remove possible remaining aftertaste left after cleaning.
In case there is a lingering vinegar smell then you can boil water in the kettle a few times. If there is a lot of scaling to be removed, you may use a stronger vinegar mixture and leave it in the kettle for an hour, or even overnight.
Plus, you can scrub the inside of the kettle with a non-metallic pad, carefully avoiding the heating element (built into the bottom).
There are certain manufacturers that explicitly warn against the use of vinegar for cleaning their products. In such cases, you can fill your kettle with water, squeeze a lemon in it and put slices of the same lemon in the solution.
Boil this water and leave it in the kettle for about an hour. Pour out the water and rinse the kettle. When the kettle has cooled, sprinkle a little baking soda at the bottom and wipe it with a clean piece of cloth. Finally, rinse it thoroughly with cold water.
Alternatively, you can put a teaspoon of baking soda and some water in the kettle and boil the solution to remove scaling. Citric acid is also considered good for getting rid of the kettle furring.
As for the cleaning the outside of the kettle, you can use any dishwashing liquid and wipe it with a clean damp cloth. While cleaning the outside, try not to scratch the finish, though. To make a stainless steel electric kettle shiny, put a little olive oil on a cloth and rub it on the outside of the kettle.