First, be sure to read up on Conditional Alerts to get a good understanding for how they're different from Broadcasts. Once you have a good understanding of Conditional Alerts, below is how you can configure some common use cases using them.
Send a Welcome Message
This is one of the simplest use cases. To send a welcome message once to each case contact you register, just create a Conditional Alert that sends for all cases of a particular case type, choose to send it Immediately, and choose to send it to the case. Then every time you register a case of that case type, your message will be sent to that case contact.
Send an Appointment Reminder
Sending appointment reminders to your case contacts is another common use case. To do this, just choose to start the Conditional Alert on a date from a case property. You will need to store the date of the appointment in this case property from your app. You can then choose to send the reminder a certain number of days before that date, and choose who to send your message to the case (or whoever you want to).
Sending a Missed Appointment Alert
This use case is a bit more involved because it requires your app to work closely with the Conditional Alert. You start off the same as an Appointment reminder, by starting on a date from a case property. You then want to send the alert the day after the appointment. Most importantly, when the appointment takes place, in order for this to work properly, a user must fill out a form in your app to record the appointment and update the appointment date case property to either be the next appointment or be blank if there is no next appointment. This way, if the appointment happens, then the alert will either reschedule when the new appointment date is set or will unschedule if it is set to blank. But if the appointment does not happen then the appointment date will not change and the alert will be sent one day later.
Sending an SMS Campaign
Sending an SMS Campaign can be accomplished by using a Custom Daily Schedule. See the documentation on Custom Schedules for more information.