[u]How Dimmers Work[/u].
I've made a 4-channel AC lighting effect but mine doesn't dim.
You must electrically isolate the lethal voltages from humans, the Arduino, and your audio system. A relay (electro-mechanical or solid-state) will provide isolation on the "output" side. Regular relays won't dim and they "click" when they switch. Electro-mechanical relays also require a driver circuit, although you can get a relay board with a relay & driver built-in.
You can get solid-state relays that work directly from the 5V low-current Arduino output (so no driver circuit is needed). A "non-zero-crossing" solid-state relay can be used for dimming.
...I made my own solid-state relays with a TRIAC and special TRIAC-driver opto-isolator, but I don't recommend that for a beginner because testing & troubleshooting can be dangerous and with power-line voltage & current you can easily burn-out parts during testing & development.
For dimming you need an AC zero-crossing detector and that also must be electrically isolated. Typically, optical isolation is used, but you can also use transformer isolation. If you build your own power supply with a regular 50/60Hz transformer (not a high-frequency switching design) you can tap-into the transformer secondary to get the zero-crossing information.
A regular-old incandescent light bulb doesn't come-on instantly so it can flicker dimly (or brightly) without the zero-crossing circuit. But you need it constantly dim or smooth-dimming you'll need the full dimming circuit and logic.
The Arduino cant read the negative half of the audio signal, in fact it can be damaged by negative voltages and/or the audio signal can be "damaged" distorted. The standard approach is to bias the input at 2.5V and with the bias, a line-level audio signal (or headphone-level signal) is just about right for the Arduino. With the bias, silence reads 512 on the Arduino ADC and the signal deviates above & below the bias. (You can subtract-out the bias in software.) There is a bias circuit attached to my [u]World's Simplest Lighting Effect[/u] post.