To save the game in a room, you have to go to bed. Your dream will last for 6 hours of the game time. In addition, you will find a chest near your bed. Open it to take some ammunition. You can change your clothes too.
If you are in the desert then you have to make a fire camp. Basic version will allow you to change your clothes, save the game and travel in a much faster way (you will be able to go to any place marked on the map). This for of resting will last for six hours. More advanced fire camp version (you can buy it in the shop) will also recharge your ammunition (only if you are out of ammo). Remember that you cannot place fire camps near water, gang hideouts, towns, mountains, while doing missions and so on.