Firstly, you will have to know the behaviours of all the common circuit elements, which is covered in practically any basics electronics course.
For linear elements, ie resistors, capacitors and inductors, you must know how to derive the response for any combination of those. Equally important, you must have a feel of the output just by staring at the circuit.
For non-linear elements like transisters, FETs and opamps, other than knowing its general behaviour, you will have to able to identify with common configurations. Generally, the more experienced you are, the easier it is for you to identify those.
There are other topics such as power supply design, filter design etc. which are also widely used.
And after learning all those above, understanding schematics is still an art. Some get it, some don't. In my university, all the above is covered in just 2 modules, and many of my friends still view schematics as hieroglyphics. IMO, it still very much depends on how widely you read. This forum is a nice starting place, and I'm still learning everyday I'm here.