Using server-side Swift and Perfect, developers can generate songs with Markov models by predicting words from a given text file. The process involves setting up a Twilio account to receive SMS messages, using ngrok to expose the local machine's web server, and creating an HTTP route to handle incoming messages. The received message is saved to a file, which is then used to train a Markov model. The trained model can be used to generate new text or songs by calling a `buildText` function with the first word of the training file, its length, and the training file itself. This setup allows developers to create an interactive system that generates music using code, making it possible to experiment with different songs and texts to train the models.