https://www.fda.gov/food/laboratory-methods-food/bam-4-enumeration-escherichia-coli-and-coliform-bacteria is a good source for most of the standard culture based ways to grow and identify bacteria. I like to use EMB agar which gives clear and easy to interpret results in 24 hours. It is not good if the levels in the water are very low. Using a filter technique is then better. Look up suppliers for media ( I like Hardydiagnostics.com ) and look under environmental tests. The new chromogenic media are good, and some growth/tests can be done in a few hours.

Dear sir,

You can plate them in various dilutions on NA plates; I do it to check water contamination. It helps.

Navnit Kumar Ramamoorthy - While using dilutions to isolate (for quantification) and grow bacteria is important, but on NA we will not know what species of bacteria are being grown. This would require at least another day for identification of the E. coli unless you can use molecular techniques.

Yes sir, You are right about that point. You approach is accurate.

Filter the water sample through a membrane filter and place the filter on any selective medium which allows to distinguish E. coli from other microbes (MacConkey, Eosin methylene blue). You will be able to see the result next day after an overnight incubation.