In a circuit involving integrated circuits, the documentation for the ic often states that if a pin is in logic 1 or high the circuit will behave in one way, and if the circuit is in logic 0 or low the circuit will behave in another way. One example i found was experimenting with the 4029 CMOS Counter ic http://www.intersil.com/content/dam/Intersil/documents/fn33/fn3304.pdf on the up/down and dec/bin pins. What i don't understand, is what the pin that is set either high or low should be connected to i would assume it would be the positive supply voltage, the negative supply voltage, or neither, but i can't seem to figure out which one.
The bottom of page 7-799 of the linked datasheet gives the thresholds for low and high input voltages given a couple of different supply voltages. As long as the voltage on the input is at most/least that value when referenced to ground the input is considered low/high regardless of what you tie it to.
Depending on the logic family you use there are different thresholds for high/low states
Here is a table that shows these different levels (image source)
You should check the threshold levels in the datasheet of your device for the intended power supply level.
In any family, connecting an input pin to ground will definitely set it to LOW and connecting an input pin to Vcc will definitely set it to HIGH.
If an input pin should be high (1) for the chip to do what you want, connect the pin to +5V (or whatever your positive supply is). If the pin should be low (0), connect it to ground.
CMOS input pins should never be left unconnected.