Dale, the rounds feed from a magazine via feed rails that are either a part of the machining of the action body's underside, or a part (lips) of the detachable magazine (clip).
The rounds are generally pushed into the chamber by the bolt, which lock into place when the bolt handle is turned down.
The chamber is loacted at that same rearmost end of the barrel, and is formed after first drilling a barrel blank for a selected caliber, like .308 (whatever) & rifling it - end to end.
The chamber end of most finished barrels is identified by the bulge that allows for the larger chamber, called the "barrel re-inforce".
The end of the rifled deep hole, selected as the breech end of the barrel, is then reamed out with an especially shaped drill bit called a chambering reamer, to a specified depth to form the chamber.
(there are multitudes of chambering reamers - a different shape for each different cartridge)
"Headspace" has to do with how deep that chamber is reamed, along with some other dimensions, like the distance from the locked boltface to the headspace datum point (different for rimmed/rimless/etc).
It can get complicated, which is why special tools & experience are need to complete a safe job.
You are not necessarily limited to the factory cartridges based on the .308 Win case (.243/.260/.7mm-08/.308/.338 Fed/.358 Win), provided you also want to step into the world of "wildcat" cartridges - where you can virtually "roll your own", albeit within that same case body.
For instance, you could build a .22 Cheetah (.22/.308), a .25 Souper (.25/.308), or try your hand at a .40 cal. It only takes determination & a lot of green paper.
