How to fire trigger only on Selected Day in salesforce

To achieve that trigger only works on selected day means,

Formatting Date

1. Date d = System.Today();
2. // you need to format date to date/time in order to format.
3. DateTime dt = DateTime.newInstance(d.year(), d.month(), d.day());
4. String todayDay = dt.format('EEEE');
5. if(todayDay != 'Saturday' || todayDay !='Sunday')
6. {
7.     // Process your logic.
8. }

Formatting Date/Time 

1. DateTime dt = System.now();
2. String todayDay = dt.format('EEEE');
3. if(todayDay != 'Saturday' || todayDay !='Sunday')
4. {
5.     // Process your logic.
6. }