Hello, Deborah, and thank you for your excellent question to Ask Extension/Ask a Master Gardener.

You should absolutely deadhead your Shasta Daisy plant to encourage it to bloom all summer and into the fall. It is best to deadhead before the flower goes to seed, if you can. And for best reblooming, don't just lop off the flower head.

Here is the technique I use: Follow the stem down until you find a new bloom emerging, and then (using clean pruning shears or scissors; I clean mine with isopropyl, rubbing alcohol) cut just above the next highest leaf. If there is no bloom developing on the stem, you should cut it about a half-inch above the ground. You might see new growth coming up at the crown of the plant. 

I've attached some images that might help if you are new to pruning/deadheading. Obviously, these are not photos of Shasta Daisies, but they are in the same family, Asteraceae, so the info is applicable. In the first photo, the red arrow shows where to find the emerging blossom. The second photo shows where to make your cut, leaving one leaf above the blossom. The third photo shows two deadheaded plants. The plant on the left had all the stems removed to new blossoming, while on the right some flowers were left. Either way is fine. Personally, I leave flowers that still look good. The blossoms will mature in two to three weeks.