You can use the following formulas in DAX to get the day of the week from a date in Power BI:
Formula 1: Get Day of Week as Full Name (“Sunday”)
day_of_week = FORMAT('my_data'[Date], "dddd")
Formula 2: Get Day of Week as Abbreviated Name (“Sun”)
day_of_week = FORMAT('my_data'[Date], "ddd")
Formula 3: Get Day of Week as Number (Sunday = 1)
day_of_week = WEEKDAY('my_data'[Date])
The following examples show how to use each method in practice with the following table in Power BI:

Example 1: Get Day of Week as Full Name
To get the day of the week as a full name, click the Table tools tab, then click the icon called New column:

Then type the following formula into the formula bar:
day_of_week = FORMAT('my_data'[Date], "dddd")
This will create a new column named day_of_week that displays the day of the week as a full name for the corresponding date in the Date column:

Example 2: Get Day of Week as Abbreviated Name
To get the day of the week as an abbreviated name, click the Table tools tab, then click the icon called New column:

Then type the following formula into the formula bar:
day_of_week = FORMAT('my_data'[Date], "ddd")
This will create a new column named day_of_week that displays the day of the week as an abbreviated name for the corresponding date in the Date column:

Example 3: Get Day of Week as Number
To get the day of the week as a number from 1 to 7, click the Table tools tab, then click the icon called New column:

Then type the following formula into the formula bar:
day_of_week = WEEKDAY('my_data'[Date])
This will create a new column named day_of_week that displays the day of the week as a number for the corresponding date in the Date column:

Note: You can find the complete documentation for the FORMAT function in DAX here.
Additional Resources
The following tutorials explain how to perform other common tasks in Power BI:
Power BI: How to Convert Date to Text
Power BI: How to Convert Date to Month and Year
Power BI: How to Convert Date to Quarter and Year