If you have never soldered before, please see the soldering is easy comic. It's a good read, even if you have soldered before.
Another good one is the Adafruit guide to excellent soldering.
These are the parts that come in the kit:
After soldering, the board should look like this:
Soldering the components
Solder the 2x20 female pinheader on the bottom of the board. It plugs in the GPIO header of the Raspberry Pi.
The rest of the headers go on top. There's only one way to fit everything in their holes, so you really can't go wrong. Make sure everything points straight up.
Only solder the 2x3 ICSP pin header onto the board if you know what it does and have a use for it.
To decide which jumpers to put on the VIN and CONN male headers, see the CONN and VIN header on the pinout page for the AVRPi-32U4.