This data sheet offers a better explanation of protocolwww.gaw.ru/pdf/Dallas_Sem/12887.pdf
Looks like the AD0-AD7 lines all need to be connected, and provide the data transfer, while AS, R/W and DS are to do with what data should be transferred. Also pull MOT low.
Then it basically functions as extended ram. You set the AD0-AD7 bits, toggle AS to set that as the address. From there you can either set all the pins to input on the arduino and toggle R/W to read the output, or set the pins to a certain byte of data and toggle the DS pin to write the data into the ic.
The address map is in the data sheet, so you'd clock in the initial time into the first 9 bytes of ram, then just let the chip update them every second. To get the time then just read those addresses.
The rest of the chips memory can be used as storage.
This all goes with a big "I think"