For OLS regression, you can solve for the parameters using algebra. Algebraic solutions are rarely possible with nonlinear models like logistic regression. Consequently, numeric methods are used to find the estimates that maximize the log likelihood function. Numerical methods start with a guess of the values of the parameters and iterate to improve on that guess. The iterative process stops when estimates do not change much from one step to the next. Long (1997) describes various algorithms that can be used when computing ML estimates.