How does a MOSFET work? (FQP30N06L)
If your drain and source are always connected, then either

your FET is broken
you've left the high impedance gate unconnected, and it's got some charge on it from somewhere, and is sitting at a Vgs high enough to make the FET conduct

Connect the gate to the source, and remeasure. If the drain and source are still connected, replace the FET.
Try this circuit



simulate this circuit &ndash; Schematic created using CircuitLab
The resistor values aren't too important, other than that R1 should be much larger than R2, to allow Vgs to get to most of 9 V when the switch is closed. When the switch is open, R1 pulls Vgs down to 0 V.
This common source configuration is preferred to the common drain you've shown when using N channel FETs, as the Vgs is easier to provide.