Give or Giving is an action performed by pressing the appropriate button when available.
After you have given an item to another hominid, as long as they haven't eaten it or caused it to disappear from the game, it is possible to perform the Take Item action to get the item back. For example - you give a hominid in your clan a Dead Branch, you can take that Dead Branch back.
It is also possible to perform the Trade Items action with another hominid. If you have an item, you can switch items with the other Hominid.