In the future, please post inquiries about electronics in general to the General Electronics section. This is the Microcontrollers section, for discussing bootloaders, custom cores, ISP programming and stuff like that - it's not even clear if you plan to use a microcontroller, or want to stick entirely with passives.
There are a whole bunch of ways to make a pot control the brightness of an LED.
1k ~ 5k pot (or rheostat).
One side of pot to Vcc, other side open, wiper to a fixed resistor, to LED, to ground. Here, the pot is in series with the LED, and you're adjusting the resistance of the current limiting resistor. So as the resistance of the pot increases, the LED gets dimmer.
LED connected normally with a fixed resistor. One side of pot connected to one side of the LED, wiper connected to the other. Here, the pot is parallel with the LED - some current will flow through the LED, some will flow through the pot; the lower the resistance of the pot is set to, the more will flow through the pot, and hence less through the LED, so it will get dimmer.
1k ~ 100k pot and an Arduino:
One side of pot to ground, one side to Vcc, wiper to analog pin.
LED to PWM pin.
Set the LED pin as output, and every iteration of loop(), read the voltage on that analog pin with analogRead(), divide it by 4, and feed it to analogWrite() on the LED pin.
By adding more parts, I could make all sorts of crazy things.