So that you might understand easier, I will paste the example I am having trouble with.

    "Wait!" Brian called out to Steven. Steven stopped to listen but did not respond. "Be careful when you go out next time, okay?" Steven disappeared into the other room, leaving his friend confused by his carelessness. Brian tugged nervously at his collar, which was dampened by his sweat. "I'll follow your lead a bit longer, old friend," he said, his voice inaudible. "I hope you know what you're doing."

My problem is whether or not each quote should be on a new line and indented. However, since all quotes belong to the same speaker, is there a need to break to the next line and indent, or only if a new speaker talks?

For visual purposes, this is what I am asking. Should the above example be written like this?

    "Wait!" Brian called out to Steven. Steven stopped to listen but did not respond. "Be careful when you go out next time, okay?" Steven disappeared into the other room, leaving his friend confused by his carelessness. Brian tugged nervously at his collar, which was dampened by his sweat.
    "I'll follow your lead a bit longer, old friend," he said, his voice inaudible. "I hope you know what you're doing."

It just seems awkward to me because in the first example, the quotes are interspersed between segments of narrative text.

There are probably lots of writing style guides that advise on this kind of thing. It is a bit tricky, isn't it?
I think I might like to indent to a new line when a new person speaks, and perhaps when there is some interspersed action. Like this.

    Wait!" Brian called out to Steven. Steven stopped to listen but did not respond. "Be careful when you go out next time, okay?" 
    Steven disappeared into the other room, leaving his friend confused by his carelessness. 
    Brian tugged nervously at his collar, which was dampened by his sweat. "I'll follow your lead a bit longer, old friend," he said, his voice inaudible. "I hope you know what you're doing."

Writers often omit the simple 'he said' stuff, don't they? And just let the reader keep track of who is speaking. eg
    Brian tugged nervously at his collar, which was dampened by his sweat. "I'll follow your lead a bit longer, old friend."  His voice was inaudible. "I hope you know what you're doing."

Look at how they do it in some novels.

Best wishes again, Clive