Chickens do not normally need to be bathed - they keep themselves clean and free of insects etc. with regular dust bathing and preening. The 'preen gland' at the base of their tail feathers (it looks like a large raised fleshy spot) contains oils that they pick up with their beak and spread around their feathers. This keeps them waterproof. If you ever pick up a chicken that has been out in the rain you should find that their outer feathers are wet, but that underneath they are still dry and toasty warm.
However, from time to time things can go wrong - most usually as a result of illness. If a chicken is sick and has a lot of diarrhea then they can be unable to keep themselves clean. This is smelly and unhealthy in itself, and dried poop can actually block the vent, but in warm weather it can also attract flies which lay eggs in the mess, and then the hatched maggots start to attack the chicken's flesh (called 'fly strike').
In situations like this, it is necessary to clean the chicken in order to remove the poop and clean the skin and feathers. The easiest way is to place the chicken in a bowl of warm water, let her soak for a few minutes, and then gently work the mess out of the feathers with your fingers. Detergent isn't usually necessary, but if you feel it is, then a drop or two of washing up liquid or children's shampoo can be added (you need very little, and you should only use it if it is really essential, as it strips the natural oils from the feathers).
HOWEVER - a BIG warning - if the chicken appears to be suffering from a problem such as internal laying / egg yolk peritonitis, if the belly or rear end is swollen, red or hot to the touch, or if you are not sure what the cause of the diarrhea is, then immersing her in a warm bath of water can be the worst thing to do. The warmth could cause all sorts of problems in an infected intestine - increasing bacterial growth or leading to swelling and perforation of the intestine. In these circumstances you can actually kill your chicken by giving her a warm bath.
If you are not certain of the cause of the problem, then it is best to stand the chicken in the sink or on the draining board, and swab the area gently with a sponge dipped in warm water. This is a much slower and more laborious technique, but it means that the chicken is not immersed in warm water.
In either case, if you need to wash your chicken for any reason, then limit the washing to the areas that are absolutely necessary, towel dry the feathers, and then gently blow dry them with a hairdryer. As long as you start the hairdryer away from the bird, bring it towards them slowly, don't have it too hot and don't leave it in one place on their body for any length of time then I have found that even the most timid of birds seem to accept a hairdryer quite happily.
In warm conditions you can roughly dry the bird and then leave her to finish air drying and preening herself, but if it is cold then you need to make her feathers as dry as possible before you let her go. Wet feathers will draw heat away from the body as they dry, and will provide no insulating effect to keep the body heat in.
Hens go broody when you don’t want them to… and won’t go broody when you do. 
