Can do I make an Arduino program that can decipher telephone touch tones?
It is possible to decode DTMF tones with only a few common external components. The trick is to turn the analog audio into a digital signal, and then check the timing between the leading and trailing edges in order to figure out which tone is present.

First, create a 1.1V bias using a voltage divider. This bias will connect to both a capacitor that is coupling the audio, as well as one of the analog inputs. Note that phone lines have high voltages on them at times, and you must have both isolation and voltage clamping in place before connecting a device to one.

Second, enable the analog comparator in the MCU. See the "Analog Comparator" section of the MCU datasheet for details. Configure the non-inverting input to connect to the internal bandgap reference, the inverting input to connect to the analog input chosen earlier, and the output to connect to the input capture facility.

Third, configure the input capture facility in the MCU. See the "16-bit Timer/Counter1 with PWM" section of the datasheet, with particular emphasis on the "Input Capture Unit" subsection. Note that there is no way to trigger the input capture on "any" edge, therefore you will need to either flip the capture edge select bit each time, or you will need to detect the tone from only one set of edges. Also note that you will need to use the overflow interrupt to increment your explicit "high bytes" counter in case the edges to be detected appear on opposite sides of the overflow.

Now that all that is done, all that remains is to compare the timing detected by the input capture with your internal table of timings and select the appropriate tone from that. But that's the easy part.