Super generally, to get the MLE for our data, we take the data points on our s-curve and add up their log-likelihoods. Basically, we want to find the s-curve that maximizes the log-likelihood of our data. We just keep calculating the log-likelihood for every log-odds line (sort of like what we do with the RSS of each line-of-best-fit in linear regression) until we get the largest number we can.