How to know it when I see a covalent network?
A good source of information on this topic is the website Tetrahedra of Structure, Bonding &amp; Material Type, from which the above image is taken.

An extreme example of the metal corner should be cesium, the ionic corner CsF, and the molecular corner $\ce{F2}$.  At the top is diamond carbon.

The network covalent apex is truncated on the basis that a network covalent material requires an element with the electronegativity of carbon or less (less than or equal to 2.55).  

Then the challenge is to distinguish a boundary between network covalent and the other three types

network covalent vs. metal

network covalent vs. ionic

network covalent vs. molecular 

Examples of network covalent compounds other than diamond and silicon dioxide include silicon carbide, silicon nitride, boron nitride, aluminum phosphide, gallium arsenide, aluminum oxide.  However, anytime there is an electronegativity difference there is some ionic component. 

Tin can exist in metallic and network covalent allotropes. 

Selenium can exist in a network covalent allotrope or as molecular $\ce{Se8}$

Going from network covalent to molecular covalent, think of how there is diamond, graphite, nanotubes, fullerenes and even small molecules like $\ce{C4}$