OK, out of your league isn't necessarily a problem, I just need to explain more clearly. Your original fritzing diagram has digital shaft encoders not pots and the shaft encoders don't use analog ports but rather digital. From the pictures it looks like you actually have pots which will produce an analog voltage and indeed need the analog ports of which there are only 6 of on a Uno. While one option would be to use a mechanical switch to switch between the pots, what probably makes more sense is to have an analog multiplexer IC (which is like a mechanical switch in that it switches more than one analog input to a single output) but it is controlled by a digital port from the Uno rather than by you physically. That meas that the software in the Uno can select which pot it wants to read without human input and can thus appear to be able to read 8 pots with only 6 inputs. Once you get the position of the 8 pots read by the Uno then what happens? At present all that I see is that the position of the 8 pots will be readable by the Uno, there isn't any indication of what it will try and do with that information as it doesn't appear to have any outputs. If all you want is for the Uno to be able to read the 8 pots, then either a mechanical switch or an analog mux should do the job. As to the connections for the Uno assuming that the red and black wires are the ends of the pot and the white is the wiper, then yes the red wants to go to 5 volts the black to ground and the white wire to the analog input port on the Uno. When the knob of the pot is moved (assuming the wiring is correct) the white wire will change from 0 to 5 volts and the Uno will read a value between (I think) 0 and 255 from the analog port which corresponds to the position of the pot.
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