NOR circuit with two switches
One of the simplest active circuits is simply a single transistor and a couple of resistors:







simulate this circuit &ndash; Schematic created using CircuitLab

R2 keeps the gate of Q1 low, so Q1 is naturally off.  That means that OUT is at the same potential as VDD less any voltage drop caused by the current draw through R1 depending on the load on OUT.  When either of SW1 or SW2, or both of them, are closed then the gate of Q1 rises above its threshold and turns on.  This drops the voltage of OUT to around 0V as the on resistance of Q1 is (or certainly should be) much lower than that of R1.

It is possible to do it even more simply without the transistor and just one resistor with a purely passive design:







simulate this circuit

When both switches are open the OUT voltage is held at (or near) VDD through the resistor.  When either switch is closed the OUT is connected direct to ground, so registers 0V.

You could also split that circuit into two separate ones and join them with a logic gate.  For instance, using an AND gate:







simulate this circuit

Or, if you invert the switch logic so it gives a HIGH when closed you can use a NOR gate:







simulate this circuit