How to quote inside a sentence in japanese?
examples-
"I said "this and that", and he replied "that and this". "
"I was told that "quote""

Question

How to quote inside a sentence in japanese?
examples- 
"I said "this and that", and he replied "that and this". "
"I was told that "quote""

Answer

「これとあれ」と私が言いました。そして、「あれとこれ」って彼が返事した。
The first one is an example of a formal situations, and the second one -> informal. Those bracket-like things are the equivalent of the inverted commas ^^
One last thing, in english, most people quote with an apostrophe, not inverted commas. Otherwise, it could turn out like your example ^_^'