No matter what you do you are going to need to get clean.
Even if you are near a large water source and can wash there you will probably need soap. You will probably want to make soap eventually but before you do that well you need to understand how it works in order to do it well.
If you of your clothes were dirty and all the dirt was water soluble you could simply wash in water.
Salt is soluble in water so if you clothes were covered in salt you could just wash them in fresh water and the clothes would be clean.
However not all things are soluble in water, this is where soap comes in.
Almost all things are soluble in water or soluble in oil. In chemistry this is called non-polar and polar.
Water happens to be polar, which means able to form charged ions and other compounds like this will dissolve in it to some extent.
Oils are non-polar and don’t form ions easily and other non polar substances will dissolve in it to some extent.
Soap is a molecule which is both polar and non polar, having a polar (oil soluble) component and a non-polar (water soluble) component.
It’s polar part is soluble in water it non polar part soluble in oils.
This allow you to use soap and water to wash out both water soluble and oil soluble material from an item.
The soap allows the oil the ability to become partially dissolved in the water and spheres of oil with soap molecules embedded. These are called micelles
The process of micelle formation looks something like this:
Once the soap has liberated the oil from the material the soap/oil/water solution has to be removed, hence the need for the removal of the water with rinsing.
Rinsing allows more oil to be removed as all of the initial oils might not have been removed. And excess soap will have more water to liberate the oil into.
Rinsing also allows anything already soluble in water to be removed. this is why a pre-rinse makes sense.
Rinsing also remove the excess soap which would otherwise attract dirt and oil and be an irritant.