Deadheading can be done by simply pinching out the old flower using your thumb and forefinger, or by using small scissors or pruners to clip off the old flower and part of the immediate stem below it.
If the flower (or flower clump) is on a long stem above the foliage, remove the entire stem at the base.
For masses of perennials and sometimes annuals that need deadheading, hedge shears can be used to shear off all the old flowers, shearing back into the foliage.
Deadheading will be your best gardening practice when trying to keep those flowers coming.