How does this amplifier work?

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When the signal at the gate changes the gate-source voltage of the Jfet then its transconductance changes how much current it conducts. But the transconductance varies from about 1000 to about 5000 for 2N5457 Jfets so its maximum amount of voltage gain cannot be determined accurately.

The load line of the circuit shows how much the current changes in the drain resistor when the gate-source voltage changes. Then Ohm's Law is used to convert the changes in the current in the drain resistor into voltage changes then you have the voltage gain result.
 
Read about how a Jfet works in a text book or in Google.
Also read about Transconductance.
 
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