Hi, IamNOT,
The M14 selector is the "wing nut" piece you have looked at in pictures. For FA fire, it is turned so the "A" is toward the shooter.
Most M14's were assembled without the selector and spring and with a "selector lock" (the round piece) in place. The selector and spring came in a little bag and could be installed, as Ken says, on the orders of the unit commander (very few commanders ordered the installation, although some did allow a few picked men to be allowed the FA option).
On the right side of the rifle, there is a connector, which is pulled forward by the front of the op rod. When the selector is rotated into the FA position, it rotates the eccentric selector shaft so that the sear release can contact the small projection on the rear sear. When the connector is pulled forward, it pulls the top lug of the sear release, pivoting it backward and tripping the secondary (rear) sear. This continues until the operator releases the trigger or until the magazine is empty. The rifle is designed so that the bolt must be fully forward and locked before the sear is released.
FYI, M14 clones use an M1 type system which has no need for and no place for the connector or the other parts. The MKS rifles have part of the selector shaft and part of the sear release welded directly to the receiver forward of their original position. The receiver "loop" that held the selector shaft and sear release is no longer there and reconversion to full auto is infeasible if not impossible.
Unless built by an outfit like MKS from scrap parts, or one of the very few other exceptions, an M14 rifle (as made by the U.S. government or one of its contractors) is a machinegun under the law, whether it will fire full automatic or not, and is subject to the registration and transfer requirements of the National Firearms Act. There have reportedly been attempts by Federal agents, at least in the past administration, to sell people M14's and then arrest them for illegal possession of a machinegun.
Other small piece of info. As a semi auto, the M14 and its clones are good rifles. In FA fire, the M14 is about worthless, as its stock design and full power cartridge simply do not allow controllable FA fire unless one outweighs the entire Ravens' defensive line.
Jim