Installing the Magpul CTR Stock
The Magpul CTR stock is one of the best collapsible carbine stocks on the market, if not the best.  The CTR stock is light weight, locks up as solid as an A2 stock, doesn't rattle like the cheaper carbine stocks, and has a high quality feel, fit, and finish.  Installing the CTR stock is straight-forward and even novice AR builders can successfully install the stock by following this how-to guide. 
The parts that are required to install the CTR stock include the CTR stock body itself, a carbine 6-position receiver extension (buffer tube) with castle nut and end plate, a carbine length spring, and a carbine buffer.  We also will be working with the buffer retainer, retainer spring, safety detent, and safety spring from the lower parts kit.
Insert the buffer retainer spring and buffer retainer into the hole at the threaded portion of the upper receiver.  The buffer retainer acts as a stop that holds back the buffer and spring under tension.  Also insert the safety detent, followed by the safety spring into the hole at the rear of the upper receiver.
Loosen the castle nut all the way on the carbine receiver extension and slide the end plate back.  Screw the receiver extension into the upper receiver, taking care that the safety spring remains in place.  Continue to screw in the receiver extension but stop when it makes contact with the buffer retainer.
Press the buffer retainer down into the hole and screw in the receiver extension until it is holding down the buffer retainer but not so tight that it is binding against the center post.  Make sure the buffer retainer can move freely up and down by pressing on the center post.
Make sure that the rib along the bottom of the receiver extension is centered along the bottom and that the end plate is aligned.  Also check that the safety spring is not bent and is properly aligned in the hole.
Press the end plate against the upper receiver so that the safety spring is compressed into the hole and that the dimple on the bottom of the end plate inserts into the slot in the back of the upper receiver.  Tighten the castle nut with a CAR wrench or armorers wrench to around 38 - 42 ft-lbs.  If you do not have one of these tools you can use a flat-blade screw driver inserted into the edge of one of the slots and lightly tap it with a hammer to tighten up the castle nut.  You may want to put a drop or two of blue loc-tite on the threads before you begin to prevent the castle nut from working loose.  Some people like to use a hammer and punch to "stake" the end plate into two of the slots on the forward side of the castle nut.  Staking basically involves smashing some of the metal of the end plate into the slot to prevent movement.  I personally don't think this is necessary for the average shooter but if you find yourself frequently diving for cover while under heavy fire, you may want to take this extra measure.
Insert the buffer spring and carbine buffer into the receiver extension.  You may need to "thread" the spring past the buffer retainer.
In order to get the buffer locked behind the buffer retainer, you may find it helpful to press in the buffer retainer with a punch or a small screwdriver.
Here is a shot with the buffer spring and buffer properly locked into place behind the buffer retainer.  The purpose of the buffer and spring is to absorb the recoil from the bolt carrier when a round is fired.  The buffer spring is compressed as the bolt carrier enters into the receiver extension, and when the spring expands the bolt carrier is pressed forward and cycles another round into the chamber.
Place the CTR stock body onto the end of the receiver extension and squeeze the inner handle to release the locking pin.  In order to get the stock into place you will have to pull down on the metal posts on each side of the locking pin and then slide the stock into place.  There is quite a bit of spring tension here so you will have to pull down pretty hard - be careful you do not pinch your fingers.
Slide the stock body into any of the six positions and squeeze the outer handle to lock the stock into place.  Congratulations, your Magpul CTR stock installation is now complete.