is the emittor what goes to the relay on the transistor?
No it is the collector the emitter goes to ground.
Since applied voltage to the base will draw current through the collector and send it out the emittor.
Yes an applied voltage to the base (through a resistor) will put a current through the base to the emitter and this will cause a current to flow from the collector to the emitter.
Sorry but I do not understand your answer as to which line the diode goes on.
It is shown in the link you said you looked at. The anode goes to the collector (just like one end of the coil) and the cathode goes to the + supply driving the relay (just like the other end of the coil).