I started off with this Kit from RobotBits.co.uk. In summary its not a bad kit to start with if you're new this. It includes all of the hardware for a basic rover, and if you get the deluxe option it includes a set of wheels, so you just need to bolt it to some kind of chasis and you're good to go. If you shop around you could probably put it together more cheaply, but that assumes you know what you need.
The neatest part of the kits is probably the mini-IO shield - that's the little board in the bottom left of the picture. It plugs into the main Arduino board (into the sockets labeled A0-A5), and gives you all the right pins to connect the servos.
Servo's are the smart motors we're going to use to drive the robot. They're not the best way to drive a robot, but they are the cheapest and easiest. Normally they need a bit of hacking to use them as simple motors, but these come pre-hacked, and you can just plug the two servos straight into the IO shield onto the set of 3 pins labeled 0 and 1. Note the black wire is the ground wire, and goes towards the centre of the main board - the white one is nearest edge of the board.
The kit also comes with a range sensor connected to the same kind of plug. Just to confuse things this might use brown for earth, but otherwise it plugs in to the next set of pins labeled 2.
Now all you need to do is grab the code from here: http://robotbits.co.uk/downloads/single_bump_Servo.pde , load it up into the Arduino IDE from here: http://arduino.cc ,hook up your Arduino to your computer via USB, and download the code into your robot.
If all is good your wheels should start spinning. It may take a few tweaks to get things set up for your robot: If it goes backwards then try switching over the cables for the left and right servos. Alternatively you can just tweak the software until its working. You'll also probably want to tweak the bump trigger threshold to make it more or less sensitive. once its working you can unplug the USB cable, and attach the battery pack - the Arduino will power up and start running your code all on its own.
That's the basics of assembling the kit. It's very easy once you know how its put together, and as everything simply plugs together you can have a practise the night before doing it with the kids! My son Alex is only four, but he's a complete robot nut, and loved "helping" on this project. He quickly learnt what each piece was, and enjoyed going though the spare parts box pointing to things he recognised, and asking what new pieces were . I think with supervision a seven or eight year old could assemble this.
In future pages I'll explain easy ways to build an easy chasis, some Arduino basics, adding some upgrades, and building some software to pull the whole thing together.