Before you can start your construction, you will need to head to your development tree with a spare point to spend. Purchase the Beekeeping technology to unlock the apiary in Manor Lords. You can build two apiaries in each region. While it is possible to construct more, this will not increase your yield so there is no reason to waste your resources or workforce.
You will need to assign workers to help look after the bees and extract the honey from the apiaries in Manor Lords. Do not waste your villagers on the bees. There does seem to be some problems surrounding apiaries. Logically, the bees should take care of themselves and all you need to do is extract the honey so your people have some extra food.
The only problem is that the apiaries do not produce that much food. Most players have reported their workers extract one honey per month from the bees and that is not enough to support your growing population. The good news is that honey is an unlimited resource, meaning there will be a constant supply.
Your hunters and gatherers can easily deplete the animal and berry deposits near your settlement. Nothing is worse than having a food supply shut down and having to think quickly so your villagers can eat. At least with apiaries, you will know that your honey supply will continue.