Data logging and basic setup - newbie help

For a school project, I am investigating how discharging rechargeable batteries in heat and with quick discharge rates affects it’s performance. So, I am testing how long the battery lasts before and after a discharge at 120fahrenheit and with a high resistor respectively. How would I set up my Arduino so that it records the voltage of the circuit while it is running? (I haven’t used any Arduino before but I have it installed and have ran some built in examples)

How would I set up my Arduino so that it records the voltage of the circuit while it is running?

The voltage of what circuit? Are you sure that voltage is the relevant thing to measure? Current is probably more interesting, I would think.

If the resistor is known and doesn't change much with temperature or other conditions, then you do only need to measure the battery voltage.

What range of battery voltages do you need? A "12V" battery will go from as high as 14.2V down to 9V when it's discharged. (That range will permanently damage many battery chemistries.)

For voltages above 5V then a simple voltage divider will get it down to the range that the Arduino can measure. For lower voltages, you can configure the Arduino to use its special internal voltage reference and use a different voltage divider.

A real-time-clock (RTC) and SD card will be invaluable. You can buy data-logging shields with both of these on board, with good library support, so you could get it working within 30 minutes of opening the box.