How can I purify dirty water, when I have no chlorine or iodine?

Drinkking water should be boiled before drinking in these conditions, if energy for cooking is available.  If there is ample rain, rainwater should be collected in sterile containers, ideally with lids so that children do not contaminate the water in the container, by putting their hands in it.  The water, however obtained, should be pured through a T shirt folded over 4 times to strain out particulate.  Harmful bacteria, like cholera, often cling to the particulate (leaves and other organic materail).  The T shirt must be cleaned and dried before being used as a strainer again. 

Another method of obtaining clean water is to put it in a clear plastic bottle, like a soda bottle.  Leave the water in the plastic bottle out in the sun for four hours or more.  The direct exposure to the UV rays in the sunlight and also the solar heat will kill most viruses and bacteria.