Hooking up a HD74LS86 IC
One very important thing to know about bipolar TTL logic (74xx, 74LSxx) is that the inputs source current, and if left unconnected will normally appear as a logic High.  For the 74LS family, you must draw about 0.8 mA (or more) from an input to make it appear as a logic Low.

Because of this, it is common practice to put switches between an input pin and ground to ensure that the input will be seen as Low.  It is also good practice to put a 5K or so pull-up resistor between the input pin and Vcc to ensure that an open switch will be seen as a High.

Also, because the inputs source current, outputs are designed to be much better at sinking current (pulling low) that sourcing currrent.  Therefore, it is best to put LEDs between an output pin and Vcc, rather than between an output and ground.

Bipolar TTL is designed to operate from 5 volts (recommended Vcc range is 4.75 to 5.25 volts).  The Absolute Maximim Vcc is 7 volts, if I recall correctly.  At some point below 4.75 volts, it will not operated correctly, but the parts will not be damaged.