Curiosity currently has an antenna that will allow it to communicate with the scientists on earth that are all waiting for this rover’s updates. There are different details that the rover may send from pictures to other things that people never thought would exist on Mars. The communication from mars to earth and vice versa would require the use of satellites.
It would depend on the speed of the data that is being sent but it usually takes about 3 minutes to about 20 minutes before data can be received. Once information has been received, it will be sent back again. Take note that without the Ultra High-Frequency Antenna, it will be harder for the rover to send information. If this gets broken, it may not be able to send any information at all.