Radio waves, of course.
Here, in addition to the story about the pictures at the end, there is a link to a detailed story about the connection in Russian.
Why are many photographs taken by Curiosity in black and white?
Well, the most reliable available is radio communication. In a vacuum, radio waves travel at the speed of light. Of course, this would mean a signal delay from about 8 minutes (when Earth and Mars are close to each other) to almost 15 minutes (when they are on opposite orbital points). But provided that packets are duplicated and verified, this is the most reliable and fastest way of communication.