I have the following project to accomplish, I have to connect an air conditioned to the internet and then controll him through the internet, so I thought to use the arduino. But I do not know how to do it, could you help me?
You need to get the schemtics for the AC unit, do some research on ethernet shields and temperature sensors.
What kind of air conditioner? What kind of voltage/power are we talking about working with (not that you'll be working directly with the unit, hopefully - but it is something to know about)...?
If the air conditioning unit has a remote control, you can program your Arduino to send the right IR commands to start/stop/adjust the unit.
An arduino with an ethernet shield and a relay like below should give basic on/off control.
Consider a wifi shield instead of ethernet if you don't want to run cable. They are more pricey though.