You will need to depress the buffer detent in order to get the recoil spring out. Most folks will want to use a flathead screwdriver as in the picture, but I and most 'manly men' typically just push it down with the thumb or thumbnail. Be aware that as soon as the detent is pressed down, the spring and buffer will launch out partway and get hung up on the hammer. Just lift the buffer up a little, and pull the spring and buffer out.
Without the buttstock, your receiver should look like the image to the left. Ideally, you will also have an armorer's wrench, as depicted above the receiver in the image.
The armorer's wrench locks onto the nut as shown. The protrusion latches into the rear notch as shown. You then use the wrench to loosen the nut from the receiver, then turn the nut via your fingers (much faster) to get a decent amount of slack on it.
Be aware that the nut is holding a plate against the rear of the AR receiver, which is in turn holding in a spring. The spring can jump out of the receiver if you don't take care at this point.
Next, you'll want to remove the buffer tube / receiver extension. However, take note that the buffer detent is located immediately in front of where the buffer tube stops on the receiver. In fact, the buffer tube's edge overlaps with the shoulder of the detent button, serving to keep it in. This is why, when you start unscrewing the buffer tube, you should keep your thumb in the position illustrated to the left. This will prevent the buffer detent from launching out, and you can then remove the detent and spring in a controlled manner.
This is how your receiver will look after having removed the collapsible buttstock.
Screw in the buffer tube until it nearly connects with the hole for the buffer detent.
Press the buffer detent down with your thumb as shown (or a screwdriver blade, if pressing hard enough with your thumb is past your pain threshold) and then twist the buffer tube until the buffer tube overlaps the shoulder of the detent, keeping it in place.
Turn the buffer tube until the rear plate is aligned with the receiver. It's aligned if the stud on the bottom of the plate is ready to slide into the recess underneath the threaded area on the rear of the receiver. Next, insert the rear pivot pin spring into the rear of the receiver. Make sure that it goes in straight, and doesn't kink off to one side or the other.
Hand-tighten the nut until the plate is flush with the receiver. The goal here is to ensure that alignment is proper.
Tighten the nut with the armorer's wrench. It doesn't have to be massively tight - indeed, some folks have cracked their receivers by over-tightening - but it's a good idea to tighten it until the nut is well beyond finger-tight.
Install the recoil spring and buffer tube. No tools are necessary; just press it in.
When sliding the buttstock on over the tube, don't forget to lift on the tab so that it's possible to slide the buttstock on. As mentioned above, lifting the tab is only for removing the stock - when simply sliding it back and forth to adjust it, press in on the lever and you can adjust it to your heart's content.
-- SeanNewton - 14 Jul 2008