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The most common approach for measuring chlorine in water is with the chemical reagent called DPD, which changes color in response to the free or total chlorine concentration (depending on the type of DPD used). You can read this color change with a simple color wheel (e.g. Hach color wheel), or use a more expensive electronic colorimeter (Hach pocket II). There are also very inexpensive test strips that can measure both free and total (combined) chlorine. This one from ITS is even approved by the US EPA.
Breakpoint chlorination is a bit more complex and requires careful monitoring of the influent and effluent, as well as the pH and nitrogen compounds. You could start by looking into manuals used in water treatment, such as White's Handbook.
Good luck! John