Measuring temperature using Arduino while walking

Hello everybody,

I have never used Arduino.
All tutorials which I found explain basics while Arduino is connected to PC via USB cable.
I want to measure temperature and humidity while walking, record it into memory, and read observations on PC from arduino.

Is it possible to do? Can Arduino write and store sensor measurements while it's disconnected from PC?

Thank you in advance.

Battery? Save your measurements to an SD card for later retrieval?