The name 'inByte' seems to imply that the variable should be a 'byte' instead of an 'int'. I would make it a 'char' instead, since that is the natural type for a variable that holds a character.
void setup()
{
// initialize serial communication:
Serial.begin(9600);
Serial.println();
Serial.println("Started.");
}
void loop()
{
if (Serial.available() > 0)
{
char inChar = Serial.read();
if (inChar == '0')
{
Serial.println("Hello");
}
}
}