How Sleeping Works
Sleeping is the only way to replenish your fatigue meter. In order to sleep you'll need either a bedroll in your inventory or an actual bed.
How to Sleep
To sleep in a bed, simply click on it. To sleep in a bedroll, you'll need to have it in your inventory. From the quick menu select the "fire" category then select the bedroll. Position the bedroll on the ground so it turns green and click to place. Click again on the bedroll to sleep or to pick it up.
How Sleep Affects Your Needs
Sleeping can only be done in complete safety when the temperature is favorable (above 0° C). This typically means in a shelter or next to a fire. Otherwise your warmth meter will drop and possibly deplete completely, causing you to start losing condition while you sleep. The bed or bedroll does provide some extra warmth, but it's good to be cautious. You cannot wake yourself up while sleeping.
While sleeping, your needs meters are still running at the normal in-game pace. If your needs run out while sleeping, your condition will begin to drop as you sleep, so be sure to be prepared for the length of time you intend to sleep.
It's possible to sleep outside without a fire. The best time for this is during late afternoon when it's the warmest. To help your odds, get as much shelter from the wind as you can, and I don't suggest doing it more more than 1 hour at a time. The weather changes quickly and you don't want a blizzard to hit while you're snoozing. And if it does, at least you won't be sleeping in it for very long.
Note: Beware the condition of your bedroll. The lower it gets, the less effective it is at protecting you from the cold.
Sleeping and Afflictions
Some afflictions will affect you in your sleep, and can even develop while you sleep (like frostbite or hypothermia). This can cause death if you sleep for too long after getting them. Some things that can cause these afflictions are sleeping in wet/frozen clothes without a fire and sleeping when the "Feels Like" temperature is too low. Make sure you plan your sleep location and time accordingly. Sleeping indoors while the temperature is above zero is always a safe bet.