Daylillies only bloom for one day hence the name. Unless the particular variety you have is a "rebloomer" it will not rebloom this year.
If you know the variety you have and who the breeder is you can find out if they are early, mid, or late season bloomers. I have all three in my yard and the plants bloom in succession so I can have weeks of blooms.
Once the flower dies and dries you can cut the flower spike down to leaf level so they are unobtrusive.