I’m an avid tea drinker, so every now and then I notice that my kettle has a build up of scale:

This is my cue to pull out the household white vinegar (ordinary cheap stuff I use for all sorts of things). I pour some into the bottom of the kettle, hopefully above the dirty mark line, and then let it sit.
One hour later, my kettle looked a fair bit cleaner, but not done yet. I emptied out the vinegar and refilled for another go:

And this was after the second hour. Much cleaner! If I hadn’t wanted a cup of tea (two hours, I mean, come on!) I might have waited longer still.
A couple of important tips:
- Don’t boil the kettle with the vinegar inside! NO, REALLY. You will notice immediately that you have erred, and there will be regret. I unplug my kettle and put a tea towel over the top so that I have two lines of defence against accidentally doing this.
- Rinse the kettle out thoroughly before boiling it again with water. Otherwise that next cuppa is not going to be quite as good as you would hope!