One of the trickiest things about the inventory when using the new graphics is that it's very hard to know where an item will be when you open the inventory, so selecting the item with the mouse is tricky.

Luckily, you can select the item that is surrounded with a yellow box by pressing the Enter key, meaning you won't have to move the mouse. So, to give an item, open the inventory by pressing I, then press G (to give), press Enter (to select the item), and click on the people/animals you'd like to give the item to.