Correlation
One very poetic aspect of VLBI is that a single antenna alone can make no sense of the noisy signal. We could relate this to the world at large, people need to interact, work together, discuss, socialize, trying to figure out the meaning of things. The correlation method multiplies the signal from two antennas with each other, and if the signals are uncorrelated the multiplied signal will average out over time. Now if a tiny bit (1/1000, remember?) is the same in both signals, we will get a positive residue over time. By repeatedly doing this, sliding the two signal over each other, looking for the exact point in time where they are correlated, we can find the time difference between the signal arriving at each antenna, and by doing so (and knowing the speed of light), we can calculate the precise distance between those two antennas.