The 74HC04 is a hex inverter. It contains 6 gates which output the logic inverse of the inverse; i.e., if you input a LOW signal, it outputs a HIGH and vice versa. VCC will be a separate DC supply voltage, usually obtained from the circuit the device is operating in. It is +5 V nominal for the 74HC04. If you have a higher supply voltage in the circuit to be modified, you can use a 7805 voltage regulator to supply the VCC.
You don't need to tie any gates together to invert the signal; that's what the inverter is for. If you wanted to, you can use two inverters to "clean up" the logic signals while keeping the output logic levels the same as the input by feeding your signal into one gate and connecting its output to the input of another gate. You don't seem to need to do this for your application.