You don't I don't think but I could be wrong, there just is different ammo period. So if you have 9mm hollow point's and you have 9mm AP rounds, then you have two different sets of ammo.
I would guess similar to the way you equipped different arrow sets in TES, just in the ''Ammo'' section rather than the ''Weapons'' section. In other words, you jump into the ammo screen, and, lets say you have a Assault Rifle equipped, you put your curser or highlight 5.56 AP (armor piercing), and press enter, 'A', whatever the select button is, and you'd load a magazine with that into your current gun (assuming your current gun uses 5.56).
It's also possible that the game will allow us to have multiple ammo types selected, though not for a single gun. To simplify, it might allow us to have it so, if we pull out a gun that uses 10mm ammo, then it automatically loads it with hollowpoints, but if we pull out a gun using 5.56, it loads it with AP rounds. In other words, we get to pre-set what ammo variant we use when we pull out a gun using that type of ammo. I think that would be kind of nice, because then we might, say, have an assault rifle that is pre-loaded for AP rounds, and we pop off a few guys wearing, say, NCR Ranger armor or Power Armor, but then get attacked by some raiders in their usual gear, and we switch over to a 10mm SMG pre-loaded for hollowpoints, and blast away at them.
In regards to hardcoe mode, I'd say there will be some types of ammo I will carry more of, probably the ones best used against un-armored enemies, but I'll keep a good stash of all types on me at all times, just in case I run into a few armored baddies. Then again, if you
know you'll be running into armored enemies, it might be a good idea to stash some of your regular ammo, and take on more AP rounds (alright, could we just call the hollowpoints shredder rounds? Such a nicer sound to the name..

) to deal with the armored enemies.
Overall though, I just think that pre-selecting your ammo variants for guns would be a great idea, as that way you don't have to worry about it, you just know ''oh, if I pull out my shotgun, it's pre-loaded with slugs, but if I run into a raider, my 9mm pistol is loaded with hollowpoints.''
A possible version of this idea would be to have each weapon itself has it's own loadout type - in other words, if you pull out a standard Assault Rifle, it might be loaded with hollowpoints, but then if you pull out a Military Rifle (or whatever they're calling the M16 now, I swear, it's name has been changed like 5 times...), it will be pre-loaded with AP rounds. So each
individual weapon would remember its ammo variant, instead of each weapon catagory. (this is confusing isn't it?)