To satisfy hunger, the tribe can harvest fruit from trees/bushes or hunt animals for meat. Foraging is simple, you designate trees to be harvested and tribe members will go and collect any available produce. To hunt, you designate a target animal, which your hunters will attack and attempt to kill. If they are successful, the animal dies and a carcass appears. You can either drag this carcass back to the main camp or butcher it on the spot. All food types decay and will eventually disappear, but putting the food in a pit will allow it to last much longer.
Hunting prey is the safer option, but you can also hunt down predators. Predators roam the map and may cause trouble for your tribe or kill off prey, so it's a good idea to deal with them. The only problem is, if they're aggressive enough, the predators may fight back...
Satisfying sleep is pretty simple at the moment. When tribe members get sleepy they will try find some bedding to rest on, but if none is available then lying on the ground will do. I plan on implementing some sort of mood mechanic, but haven't decided how to do it yet. A tribe member's mood would be affected by factors such as whether they had a comfortable sleep, injured a body part or had a family member die recently.
Speaking of family, that has been implemented as well. Every tribe member is part of a "family" within the tribe. If there is a male and female within the family, they may produce a child. Currently the male walks up to the female, talks to her and she becomes pregnant... I'm still working on this part. Animals can be part of a family as well, and will tend to stick together (until you start chasing them around).
OK, enough blabbering. Here is a gratuitous in-game video of lions at an all-you-can-eat buffet: