Asparagus is typically done cooking once it reaches a rich bright green. Once it's bright green it should be tender yet crisp. You can continue to cook the asparagus to soften it further if that's what you prefer.
The cook time will vary depending on the size and thickness of your asparagus spears. For small thinner spears, they'll cook up in around 3 minutes, medium-sized asparagus take around 6 minutes, while large, thick asparagus spears will take closer to 10 minutes to become tender. It also comes down to personal preference. Do note that asparagus can overcook very quickly, so keep an eye on them in the pan. You can test for tenderness by poking them with a fork.
The soy sauce adds an extra element of flavor. You can omit it if desired or melt 2-3 Tablespoons of butter in the skillet to coat the asparagus in instead.