I'm very new to electronics. Can someone explain to me how pins work, or direct me somewhere I can learn about how computer component connectors work?
My goal is to run a computer fan directly from some power source (like AA batteries), without the motherboard or any other computer components.
A typical computer fan has three wires. This is a link to such a fan's connector. They are powered from 12 volts DC. When just powering the fan with straight DC power the tachometer line is not used. Generally but not always the power is red + and common is black -, note the connector orientation shown in the link. Many newer fans have 4 wire connections. I assume you have basic 3 pin fan(s).
Something to consider when using batteries is a typical basic fan draws about 150 to 200 mA of current at 12 volts so plan your batteries accordingly. For example using AA alkaline batteries you would need 8 batteries in series to get 12 volts.