When it comes to writing speech within dialogue, a fair amount of confusion seems to prevail.  Of course, which convention of English Grammar is deemed correct depends in which part of the world you are writing.  It also matters greatly whether you are writing fiction or non-fiction.

Writing non-fiction:

British grammar: Don’t use quotes within quotes. Use reported speech within double quotation marks at all times.

“That’s when the mechanic boasted he knew everything about engines, but to be honest, I wasn’t convinced.”

US grammar: It is acceptable to use single quote marks within double quotation marks.

“That’s when the mechanic boasted, ‘I know everything about engines,’ but to be honest, I wasn’t convinced.”

Fiction:

If you want to be geeky about it:

British grammar: Either use double quotation marks within double quotation marks, which looks clunky or use reported speech within double quotation marks.

“That’s when the mechanic boasted, “I know everything about engines,” but to be honest, I wasn’t convinced.”

“That’s when the mechanic boasted he knew everything about engines, but to be honest, I wasn’t convinced.”

US grammar: Use single quote marks withing double quotation marks.

“That’s when the mechanic boasted, ‘I know everything about engines,’ but to be honest, I wasn’t convinced.”

But in modern works the opposite is also acceptable, provided your use of speech marks is consistent throughout your work.

‘That’s when the mechanic boasted, “I know everything about engines,” but to be honest, I wasn’t convinced.’

Otherwise: dialogue within fiction is an art form; how we construct that dialogue using grammar is also an art form. Dialogue in fiction should be seen as an extension of a particular character’s personality—how we speak can define how others see us. I often use different grammar conventions for separate characters, this way the reader can identify who is speaking without me having to always use an identifier.

Personally, I normally use either reported speech or single quotes within double quotes, (I think this convention looks clean and everyone understands what it means).  Which I convention I use will depend on the character, their personality, and what I want to convey through that particular piece of dialogue.

However, (and grammar geeks round the world will choke at this) when it comes to fiction, provided the grammar fits your writing style and character personality, and provided you are consistent throughout your work, anything goes.

The main test is whether the grammar you use clearly conveys the meaning you intend to convey.

Regards,

Nick