Use column selection. Column selection is one of the unique features of Sublime2; it is used to give you multiple matched cursors (tutorial here). To get multiple cursors, do one of the following:
Mouse:
Hold down the shift (Windows/Linux) or option key (Mac) while selecting a region with the mouse.
Clicking middle mouse button (or scroll) will select as a column also.
Keyboard:
You now have multiple lines selected, so you could type a quotation mark at the beginning and end of each line. It would be better to take advantage of Sublime's capabilities, and just type ". When you do this, Sublime automatically quotes the selected text.
Type esc to exit multiple cursor mode.