My first arduino project: what parts do I need to create the simplest vehicle

That's what it looks like to me as well. However, this might be a new design - Compare carefully to this picture, and you'll see that those headers are offset (and therefore have black plastic bits on the male headers), while yours appears to use stackable headers, which never have black plastic bits on the pins, because then you couldn't put them through the holes!

Try moving it just a little to the side, so the shield PCB rests on the female headers (as if you could push it all the way down).

If you've got less than the pitch of the connectors between the bottom of the male pins and the Arduino PCB (or the male pins are touching the PCB) then the pins are too long, your female headers are too short, or you need the black plastic bits for spacers. In this case, I'd probably just cut 4 pins off of a male header strip, pull the black plastic bits off, and then push them onto the corner pins on your XBee. You could also carefully trim the pins to be a little shorter, or you could get back in touch with Marcus for a replacement which matches the picture.

If you've still got 0.1" between the bottoms of the pins on the XBee and your Arduino PCB, then you're either not pushing hard enough or you've got a piece of something (probably a broken wire) stuck in the bottom of one of your female headers. In this case, you need to replace the plugged header on your Arduino.

Does this answer your question?

If you want the thing you're making to be a "proper" Arduino shield, you can buy something like this "Protoshield" board from Adafruit:

http://www.adafruit.com/products/51

Other vendors sell similar boards. It's basically a bit of perfboard that's designed for mounting components, but with the header pins already setup to "stack" onto an Arduino.

If you don't need an actual shield that stacks onto your Arduino (that is, if you're going to run cable of some sort from the Arduino to the rest of the device, or if you're going to use one of the the super small Arduino clones) then you have a couple of options:

1. Build it on perfboard. You can get perfboard that's designed to map very closely to the experimenters breadboards, or perfboard with one small copper pad per hole.

2. Make your own PCB (printed circuit board), using one of a couple of techniques. You can use chemical etching, after you either draw traces on the copper clad board with a resist pen, or use the laser printer technique mentioned by Majenko. In either case, it involves soaking the copper clad board in an etching agent that dissolves all of the copper, except the part covered with "resist." What's left are your PCB traces.

   Or, if you have an active hackerspace or hobby electronics community in your area, you might get lucky and find somebody who has built a DIY PCB Mill, who could mill the board for you. Or if you're really enthusiastic, you could build your own DIY PCB Mill. :-)

3. Farm out the "fab" of your circuit board to a specialist. This involves creating the PCB layout on a computer using something like Eagle, and then submitting the file to the fab, along with payment, and then receiving a package of boards a few days later. This may be a little too expensive if you only need one board... this is more for people who are building things to sell in volume. But some hobbyists make it economical by pooling their orders and splitting the cost.