Welcome!
How little is "nothing"? Any programming in spreadsheets for example? Have you used a solder iron?
You can start by downloading the Arduino development enviroment and see if you can enter a program syntactically correct. (using the "verify" which compiles the program). Look LED flash http://arduino.cc/en/Tutorial/Blink and at the button count program http://arduino.cc/en/Tutorial/ButtonStateChange to start with. At least that part is free.
Of course, if you buy a kit (a modest investment, and you can stop there) and can get the above to work, then you are well on your way to succeed with the rest. A kit will include a few components so you learn to distinguish a LED from a resistor and so on, and the breadboard means you need not solder yet.
Then, if all is still well, the project continues:
- Buying a GPS chip, getting the serial to talk to it
- Buying a "large" memory chip (SD?) and store/retrieve data
OR - Buy a wifiboard and send the data to somewhere else for logging.
About 3 months of hobby work