Is it possible to create your own ammo?

I haven't found this option at the weapon crafting station, which was my first thought, and a brief google shows Fallout: New Vegas had it, so I'd think FO:4 would have it too. I don't see it anywhere though. If there's no way to craft ammo, what's the best way of gaining/hoarding lots of ammo?

You can craft ammo with the Contraptions Workshop DLC using the Ammunition Plant.

I have yet to try this in-game myself, so this answer isn't very detailed, but I'm surprised no one has written a nice answer about it yet, so let me at least note it.

The only special ammo in fallout 4 you can create is for the syringer rifle.

However, the shops and the wandering caravans tend to hold a lot of ammo.

Random caravans will show up in your settlements, such as sanctuary. Also the weapon dealers in Diamond City and Good neighbor tend to carry a lot of ammo.

Finally there is the scrounger perk that lets you find more ammo as loot.