How can predictions be made from correlations?

Yes, predictions can be made from correlations. For example, one can find predicted values via this formula using correlation:

predicted y = (rSy/Sx)X - (rSy/Sx)xbar + ybar
...where r = correlation, Sy = sd of y, Sx = sd of x, and X is the variable.
Also: xbar = mean of x; ybar = mean of y.

I hope this helps.