Dialogue Rules for Presentation

The first (and main) rule is Be Consistent.  In other words, while most dialogue is presented on an indented new line within quotation marks, 

   'Like this,' she said.

you might see dialogue presented with dashes and no indent

- Like this, she said.

- And here's some more, he added afterwards.

And there are other variations that I've seen, but the first version is most usual and the easiest to read.  So long as you are consistent - ie chose one method and stick with it - you'll be fine.  

When it's a new person speaking you always start on a new line.  However, if it's the same person speaking you don't always have to start on a new line, but can imbed the dialogue into the same paragraph.  

   'Have you eaten yet?' Meghan said.

   'No - what's for dinner?' Michael asked.

   'Boiled lamb and pickles,' she replied, wiping the carving knife on her apron.  The rain lashed at the windows, blown sideways by the unforgiving wind that whistled and whined down the chimney.  'Pickles are from the farmers' market.  They're good 'uns.'

Because the comment about the pickles comes attached to the previous bit of dialogue from Meghan, we assume that it's still Meghan speaking.  If it had been on a separate line, and indented (as below), we'd have assumed it was Michael talking. 

   'Have you eaten yet?' Meghan said.

   'No - what's for dinner?' Michael asked.

   'Boiled lamb and pickles,' she replied, wiping the carving knife on her apron.  The rain lashed at the windows, blown sideways by the unforgiving wind that whistled and whined down the chimney. 

   'Pickles are from the farmers' market.  They're good 'uns.'

Sometimes a character has a long, long speech and rather than have them ramble for page after page with no paragraph break, you need to give them a rest.  You indicate this by NOT closing the quotation marks on the previous paragraph of speech.

   '.. Boiled lamb and pickles, that's all we had to eat, in those days.  You youngsters don't know you're born, what with burger this and pineapple that. A juicy gherkin was as exciting as  condiments got in those days.

   'Mind you, I still remember that time I ate some piccalilli.  It was on a Tuesday, right after the farmers' market...etc etc.'

   'What fascinating stories you tell, Meghan,' Michael said, suppressing a yawn.

So if the first rule is Be Consistent, the second rule is Make It Clear.  If any reader ever has to work out who is speaking, you've failed in the dialogue presentation.