With today's technology the easiest way to establish an interface between the brain and a computer is to look for brain signals related to movement. When you think of moving a hand an electrical signal is generated in a specific part of the brain and researchers have perfected their capability to intercept these signals. The problem is that even for this very specific type of signals the electrical activity of the brain is quite complex and singling out those exact signals from the thousands of others remains challenging.
One can be more accurate if the sensors picking up the signals are placed directly "in the brain". This is done using sensors array implanted on the surface of the brain with tiny spikes entering the brain in sub-millimetric way.
Using this approach researchers demonstrated few years ago, in 2012, the possibility to control a robot to perform like a "hand", picking up a glass, taking it into reach of the paralysed patient to let her drink from a straw.
Now a team of researchers at Stanford has perfected this technology to the point of detecting the intention to select a character on a keyboard displayed on a screen (as part of the Braingate Initiative). The paralysed patient looks with her eyes at the screen and that particular character. This induces tiny movements in the eyes that are controlled by muscles through the electrical activity in the brain. This activity is picked up by the array of sensors implanted in the brain and it is decoded to find intended character.
The experiment has shown that a paralysed patient can "type" with his "mind" at a speed that compares to the one of a person using a keyboard.
Clearly this is a significant result coming to the help of people that have lost the possibility to talk along with being paralysed.
Notice that there is still some training needed. The person has to learn to use the interface, it is not like connecting the sensors to the brain and the computer can detect the intention. Both the person and the computer need to do some training to achieve good result. Also, the signals intercepted are the ones that would activate the muscles (even though in case of paralysed people the communication channel is broken so the muscle does not receive the signal). It is not really like reading the mind of the person. We are still quite far from that.