Task dates are determined by the project calendar and the task duration. You can schedule tasks to start or end on a weekend day, in which case duration will be based on the number of working days. You can also schedule tasks occur on a weekend.
There are a couple of ways to schedule tasks on a weekend (assuming that working days are weekdays):
Schedule the task manually; recommended for one-time tasks.
Create a working hours event for the specific weekend on the project calendar; recommended for on-time tasks.
Note that you can change a task's base calendar only for leaf tasks.