The Scrum Guide says about a Sprint that it's "a time-box of one month or less". So based on that, the sprint duration can be whatever you want it to be in that duration interval, but people usually chose weeks as their Sprint duration: one week, two weeks, three weeks, one month. And yes, that includes weekends.
When people say 30 days Sprints, they usually mean a one month Sprint, including weekends. If you choose 30 working days as the duration, that goes beyond the recommended one month maximum length for a Sprint (30 working days is about one month and two weeks on the calendar).
The most extreme case I've seen was 2 days sprints, where you had one Sprint on Monday and Tuesday, another Sprint on Wednesday and Thursday, and a Sprint on Friday and next Monday, then a Sprint on Tuesday and Wednesday, and so on... whatever floats your boat I guess :)