As you progress in the game you will gradually unlock new ammo types and alternate fire modes for the various weapons. I don't want to include too many spoilers here, so I'll just cover the basics. Check the Upgrades page for details.
Once you have unlocked different types of ammo, press the weapon select button multiple times to cycle through the different ammo types. For example, when using the bow, press 1 on the keyboard or D-Pad Up on the controller until the arrow type you want is selected. Then aim and fire as usual. For the shotgun, press 3/D-Pad Left repeatedly to cycle through the different types of shotgun ammo. And so on.
When you select the bow and hold Aim, you'll see the ammo counter at the top right corner of the screen. Notice the icon in the middle for normal arrows and the count: Lara now has 40 arrows.
Press Bow Select again (1 on the keyboard or D-Pad Up on the controller) to switch to fire arrows, provided you've unlocked this upgrade. The ammo count doesn't change, since you haven't fired, but see how the icon changes to the fire arrow icon. You can also see the flaming arrow that Lara is holding.
Press Bow Select again (1 on the keyboard or D-Pad Up on the controller) to switch to explosive arrows, again, once you've unlocked the upgrade. The icon in the middle of the ammo counter changes to the explosive arrow icon. Explosive arrows are basically normal arrows with grenades taped to them. So the count also changes, since you can only shoot as many explosive arrows as you have grenades. Here, I have 7.
Press Bow Select again to switch back to normal arrows.
Again, it works the same way with other weapons. Just press the weapon select button for that gun to cycle through available ammo types or accessories.
Rope arrows are the exception. Once you've unlocked them in the Cliffside Village level, aim at a rope-wrapped object like this one. You'll notice the targeting reticle changes to a red dot with three radiating lines. Press the Alternate Fire button (R2/RB) or Space on the keyboard to shoot an arrow trailing a length of rope which then attaches itself to the rope-wrapped object. Rope arrows do not use up any actual arrows, so you'll notice the icon changes and the ammo count disappears.