Seems to:
1. move up a text block ({)
2. enter insert mode on line above cursor (O)
3. enter a LaTeX string (\begin{quote})
4. exit insert mode, move down a block of text (<ESC>})
5. enter insert mode one line below the cursor and enter the closing LaTeX string (\end{quote})
6. exit insert mode and move back up to the start of the text block, enter visual mode, move back to the bottom of the text block and also selecting it (<ESC>{v})
7. while still in visual mode run a normal mode command that moves to the end of the line and inserts "\\" at the end of the line.