How to use Arduino as RC Receiver
EDIT this answer explains how you can put a Arduino between a (1 ppm pin per channel) RC receiver and a RC receptor. This allows for smart features (like autonomous control with RC overrule, or sensor based corrections,..)
It seems it is not the question of op.

What you want is easy but there are some pitfalls.
I can make a long story short by these links

http://rcarduino.blogspot.be/2012/01/how-to-read-rc-receiver-with.html
http://rcarduino.blogspot.be/2012/01/how-to-read-rc-receiver-with_20.html
http://rcarduino.blogspot.com/2012/04/how-to-read-multiple-rc-channels-draft.html  

if you are serious about RC this may be of your interest to
http://rcarduino.blogspot.be/2012/01/how-to-read-rc-receiver-with_25.html  

I also converted this info in a library you can find here:
https://github.com/jantje/ArduinoLibraries/tree/master/RCLib

And for stackexchange policy here the hightlights.
If I look at the picture you added you have a 6 channel ppm receiver. Each ppm channel you want to read must be connected to a interrupt enabled pin of your arduino (The drawbacks of software enabled interrupt pin is another discussion).
The high time of the ppm tells how high or low your lever is on the remote control.
You can then have arduino do with this info what you want. For instance use the servo library to generate a ppm signal out to servo's and ppm driven motors.