Hold Q. Throwables appear on the left of the screen. Use the mouse to hover over the one you want and release Q. To verify that you have selected the right one, right-click, which shows your current weapon, ammo, and throwable in the lower-right of the screen. Click the scroll button to throw your current throwable.
The only possible issue I can imagine is that you haven't actually crafted the throwable you want to use. Each will show amounts x/y below the icon, where x is how many you have and y is the max you can carry. Make sure x is at least 1.
You always have an infinite number of rocks, and T always throws a rock. If you want to throw a grenade, knife, etc., you need to click the scroll button on your mouse.