The DS1302 is a real time clock but works with a trickle charger for battery back up. Unless you specifically want that feature, most folk start with the DS1307 or the more accurate DS3231. DS1307 is available in DIP8, but the 3231 comes in a SOIC package - just use a SOC to DIP adaptor
There are libraries for both for example DS1307RTC (the DS1307 and DS3231 are pretty much interchangeable with these libraries if you just want the basic times and dates)
You will also need the Wire.h library for comms and TimeLib.h to really get at the functions.
If you really want to get down to basics and work without a specific clock library, have a look at
http://tronixstuff.com/2014/12/01/tutorial-using-ds1307-and-ds3231-real-time-clock-modules-with-arduino/Have a look at Paul Stoffregens Github repository (look for DS1307RTC library)
Jack Christensen has a TimeZone library if you want daylight saving etc.
Just using the DS1307RTC library and one of the examples like ReadTime or SetTime will get you started
The TimeLib library takes the time from the RTC - nice combination