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Look on Instructables, someone posted how to do it there
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Is it possible to use an Arduino to dim a lamp using its 1...10V Control?
What does "its 1...10V Control?" mean?
Usually I would use a potentiometer, but I want to automate this.
There are electronic pots that can be controlled by the Arduino.
hi i think i know what the 0-10v controll means and its a protocal used many years back by ligting egineers.
but dimmerable VCA's for TL bulbs still use it.
but i think its possible but your arduino uses 5v or 3.3v depanding on the bord you have.
so you will need to have a separte power supply dat gives 10V.
and i think you need some transitors. but there are many other poeple that know this as i'm not realy good with hardware.
Greensprings:
who is using 230 to make light? are you an arc wielder?
like , all over Europe.
and you dont use 230V for arc wielding but 3phase 380V.
buy an SSR that can operate with 5v signal .
then pwm it to regulate power to the lamp.
if you have a rotary dimmer, you could mount a stepper or servo on the knob.
and you dont use 230V for arc wielding but 3phase 380V.
I do arc welding regularly with 120V AC, single phase.
PaulS:
I do arc welding regularly with 120V AC, single phase.
Well sure you do, but these guys are talking about arc wielding - that's serious business and apparently needs 380V 3 phase 
See if this is what you need:
PaulS:
What does "its 1...10V Control?" mean?
There are electronic pots that can be controlled by the Arduino.
Fairly common type of fitting in commercial installs.
All fittings are fed with a constant 240v ac and the control 0v gives Off and 10v Full on.
Antwhere in between is the dimming,usually controlled by Cbus or similar.
There are other types but they esentially operate the same fashion.
So I imagine the op would like to generate a 0-10v signal.
Questions are, is the control ac or dc and secondly, is the op aware of whether the light sinks or source the 0-10v control.
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if you looking to better tools working with 110V/220 As well with easy and safe to connect and simple to program i recommend you to see this
this device allowing you to control AC voltage "on off or even as dimmer " simply by sending PWM rather than right a complex code which allow you to integrate it with more advance project.