In the example above, the speaker says "walking down the street, playing with her phone". This describes a person who is doing both of those actions at the same time. Also use this format with "sitting":
He was sitting at his desk, reading something on the computer screen.
This doesn't work for all actions, but when one of the actions is "walking", "running", "standing", or "sitting", you can use this type of sentence to talk about doing two things at once.