The breakout connector is plugged into the breadboard at the end with the lower row numbers. Also the + buses will connect with the +5V and +3.3V pins on the connector.

It's obvious which end of the ribbon connector goes into the breakout connector. If the breadboard is oriented with the connector at the bottom, pin 1 of the cable (the red stripe) is on the left.

The position of the other end of the cable is also obvious, pin 1 should go in where the Pi board has P1 printed.

Just to be sure, double check with a continuity tester. The GND line of the breakout connector should connect to the rim of the RCA video connector.

When powered up, the power LED on the breakout connector will glow.

Assuming you have Raspbian installed on the Pi, follow the instructions at the wiringPi site to download and install.  You probably will need to install git-core first. Test using the gpio utility and also the pintest program.

There is a blink.c program in the examples/ directory. Compile it with gcc thus:

gcc -O -o blink blink.c -lwiringPi

The -lwiringPi tells gcc to link with the wiringPi library. Connect up a 220Ω resistor in series with a LED between P0 and the +3.3V bus. Don't use a LED with a forward voltage greater than 2.5V or it will not turn on. Run it with

./blink

This is somewhat dependent on your Linux infrastructure, so I can only provide a starting point like here. You may need install extra packages, start services, and deal with the firewall on your Linux workstation, if one is running.