Mix 1 cup water with 1 cup of brown rice flour. Place this mixture in a shallow glass bowl and cover it with cheesecloth. Set this outside on a warm day for several hours or overnight. Leave it in a warm place for 2 to 5 days, depending on how long it takes to bubble and sour. It is a good idea to stir the mixture occasionally, as the rice flour will settle to the bottom of the bowl. If it starts to dry out - you can add more water. Once it has a good sour aroma and is full of bubbles, it is ready to use. Each time you use the starter, replenish it with a mixture of equal parts flour and water.
This is what gluten free sourdough starter looks like. The rice flour settles to the bottom. But there are bubbles floating on top of the water and it smells nice and yeasty.
This process takes advantage of the wild yeast cells that occur naturally and are floating in the wind. Now - as a disclaimer - I need to explain that I live in rural Montana. There isn't any air pollution here to speak of. I don't know how this process will work where you live, but it is probably worth a try. I am pretty sure wild yeast cells are everywhere - even in the city. If you don't want to risk wasting an cup of rice flour - maybe try using a half cup of rice flour.
If, at any time your starter turns pink or moldy - you need to throw it out and start again.