Start by adjusting "Data usage" settings
Most important thing is to set limits, this will prevent accidentally use more data than the plan has. In Android, there is an option in settings to limit data usage and adjust a warning level. These settings can be found from Settings > Data usage. I've set 4 GB for data limit and 3 GB for warning limit.
Under data usage menu there is also Data saver to limit background data usage for the apps. It's also possible to limit certain apps and whitelist others. The only risk included here is that messaging apps like Whats App may not work when the screen is turned off, that it's good to whitelist all the messaging apps. …show more content…
In Youtube app settings you can limit the HD-playback only for Wifi connections.
Get rid of ads by using AdAway (Rooting required)
A study made by Simon Fraser shows that add's can take up to 25 percents of the bandwidth. Google makes money from ads so ad-block apps are not allowed on the Play Store. There are some browsers with built-in ad-block capabilities like Opera mini. I use AdAway, it's available only for rooted android phones.
Compress those web pages
Google Chrome and Opera have been offering a possibility to compress pages and images before downloading pages to the end users device. Opera also has a stand alone app Opera Max that can compress all data by routing the connection through a compression proxy. To enable compression in Google Chrome go to Settings > Data