When we were suddenly attacked by ticks a couple of years ago I had to find a way of removal that did not leave the head in the skin. I found one of these at my vet's office and it works well. You just slide it around where the tick is attached to the skin and twist it once and pull. Out it comes head and all! Yuck! Then I flush them. Never touch them with your fingers as they can be full of germs.
Amazon.com: Tick Twister: Pet Supplies