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You must have a cellular plan that supports personal hotspots. This method will share your phone's cellular data connection with the computer you are using, allowing you to bypass the regular network.   Click here for instructions on creating a hotspot on an iPhone.  Click here for instructions on creating a hotspot on an Android phone. This is the easiest way to share your connection, though you can also turn your device into a wireless access point and connect via Wi-Fi. Click the Network icon in your System Tray (Windows) or menu bar (OS X) and select your phone. The computer will connect to the phone's network so that it can use the internet. Once the computer has connected to the phone's network, you can use your web browser to open Facebook. Since you're connecting through you're cellular data plan, you are safe to log into Facebook securely. When you load a webpage on your computer, it loads the desktop version, which typically requires much more data to be transferred than the mobile version of a website. This can become a problem if you have a low data cap or are close to using your monthly allowance.   Click here for instructions on checking your data usage on iPhone.  Click here for instructions on checking your data using on Android.
Enable the personal hotspot function on your smartphone. Connect your smartphone to the computer via USB. Select your phone from the computer's Network menu. Browse to Facebook on the computer. Monitor how much data you are using.