Correct measurement for chicken broth powder to water

The basis for any sort of Japanese soup dish is going to be dashi stock, a stock made of fish and seaweed. It has a much lighter flavor than chicken broth, so you might not have identified it easily. You can buy it in a powder form for convenience, and it can be sprinkled into other liquids rather than reconstituted.

This recipe is for soba with a dipping sauce, but it'll give you a good idea of the flavor profile you're looking for: Dashi stock plus kaeshi, which is made of soy sauce, mirin, and sugar (and simmered so it's not strongly alcoholic).

A piece of muslin/cotton/fine-tissue-of-your-choice will do the job nicely.

You can easily find it in kitchen stores or online.