To add to the answers above, here's how you can use the right kind of quotation marks on your computer.
On Mac, while using Russian keyboard layout:
= to type
= to type
num lock, then push and hold
alt, then type these sequences of numbers on the numeric keypad:
0171 to type
0187 to type
0132 to type
0147 to type
Another difference between Russian and English quotation marks is where you put the period. In English, the period is put inside the quote: "Like this
." In Russian, the period is put after the quote: «Вот так
It should be also said, that the outstanding majority of Russians don't use the correct quotation marks on the Internet. As far as I know, the
" symbol didn't use to be a quotation mark either (the English quotation marks are
”), and is only used now due to the fact that typewriters lacked the proper signs. However, it is accepted now in English, and is widely used in Russian, despite the snobby attitude the graphic designers have towards it.