Beginning in the Shipyard (Station) you have access to that particular station's Store. To access the store, look in the lower right corner of the screen and press the Store button.
Once you click on the Store button, you'll see a screen open like that below. Click the checkbox on the right that says "Trade Goods"
Once you click Trade Goods, you'll see ammo and ore pop up in the right hand side of the screen. This is the store inventory (not your station inventory) and shows what is available to buy in that given category. Below is an image of the Trade Goods available to be purchased (I expanded the image of the ammo options.
Each ammo option fits a different weapon type.
Kinetic Ammo: (3 bullets): Kinetic weapons tend to fire in bursts, with a delay between sets of bursts.
Guided Missile: (crosshair over missile icon) explosive damage, tends to fire individual rounds with a delay between each round.
Non-Guided Missile: (missile icon) explosive damage, tends to fire individual rounds with a delay between each round in a straight direction.
Click on the icon of the ammo you wish to purchase, and you'll see it drop into your shopping cart (center column)
As you click and move items into your cart, the Price at the bottom of the screen will start to increase. If you have more money (Credits) than the Price, you can make the Deal and purchase the ammo.
Next up, moving the ammo to your ship.