iPhone 5s using too much data on Wi-Fi
Apology:
It has come to my attention 3 years since this original post that my original answer did NOT meet OP's requirements. To the best of my knowledge, there was no easy way to do what OP was requesting in iOS 10. This new answer refers to new settings introduced since this question was asked to provide useful information for anyone else viewing this. Again, my other answer DOES NOT meet the requirements of the question.
NEW ANSWER (works starting on iOS 13):
- Connect to the WiFi network you wish to have limited bandwidth on.
- Click the "i" info button next to the network as you are connected to it.
- Underneath "Auto-Join" there is a slider marked "Low Data Mode". Switch the slider to on.
That's it. For a step by step guide with screenshots, see this link.
EDIT: Below is my original answer (for posterity). It describes turning off "Wi-Fi Assist" which, while reducing cellular data use, DOES NOT answer OP's question of reducing data use. For Apple's built-in solution to reduce data usage on cellular, see my other answer.
Go to settings -> cellular. Scroll down past the list of apps to "Wi-Fi Assist" and turn it off! This has been a huge problem for lots of people. Wifi Assist is turned on by default. When it's on, whenever your mobile data is faster than your wifi, it uses your mobile data without telling you. Your problem should disappear after you've completed this step.