I've never built anything like that, but, there are two ways to do it. You can use a Hall Effect device, which is a solid-state device that responds to magnetic fields, or you can use a Current Sensing Transformer, which is a coil around the current-carrying wire (which again picks-up the magnetic field). These devices will put-out a voltage that's proportional to the current. With either method you don't need an electrical connection the the AC power, so it's (relatively) safe.
If you are willing to assume the voltage remains constant at about 110/120VAC, you don't need to measure the voltage. (From the measured-current andknown-voltage you can calculate power.
The Arduino's analog-to-digital converter reads DC voltages from 0-5V. The Arduino can be damaged by negative voltages, or by voltages greater than 5V.* Take a look at the [u]Analog Read Voltage Example[/u]. Once you get your current sensor working, you'll have to measure, calculate, and calibrate your ADC readings (0-1023) to indicate amps. The ADC is very simple, and once you understand how the 0-1023 reading is linearly proportional to 0-5VDC, you should be able to figure-out your program (sketch).
You'll need an ammeter to calibrate you device. You may be able to do it with calculations, but it would be a very good idea to confirm that your device is calibrated correctly. If you get a clamp-on meter you won't have to cut any wires or touch the AC voltage, but you may need to rig-up something since the clamp-on meter needs to go-around only one wire. (The magnetic field is canceled-out with the current flowing in opposite direction through two wires.).
The Hall Effect device is a DC device. It's only going to read one-half of the AC waveform, but that's generally OK since the negative & positive current on a AC line is usually the same. (Or you could use two Hall Effect sensors, or maybe somebody makes a dual one for sensing AC?) The transformer is an AC device, so you'll have to rectify it to get DC (probably with a "precision rectifier" circuit using an op-amp).
It's also very likely that you'll need an op-amp to boost the signals from the transformer or Hall Effect device get the voltage in the 0-5V range. (You'll have to check the specs on the device you choose.)
P.S.
You'll also need to figure-out how you want to display the results if you are not gong to read them with the computer over USB, and if you want to measure energy consumption (power over time, or Watt-Hours), of course that will complicate your software.
And if you are not already familiar with it, take a look at the [u]Kill-A-Watt[/u] gizmo. It may give you some ideas, or you might want to forget about building this thing and just buy a Kill-A-Watt. 