Since humans can get diseases from ticks, it is best not to remove the tick with your bare fingers. Use either tweezers or a tick removal instrument.
To safely remove a tick:
Try using an alcohol swab, which may irritate the tick and cause it to loosen its grip.
Grab the tick with the tweezers where the mouth enters the skin. Do not grab it by its body.
With a slow steady pull, remove the whole tick without twisting it as you pull.
Deposit the tick in alcohol to kill it.
Clean the area with a disinfectant and apply an antibiotic.
Wash your hands thoroughly.
Swelling and skin irritation may occur after the tick is removed. This is a reaction to the toxic saliva of the tick, not due to the head remaining in the wound (which rarely happens if you grasp the head of the tick during removal).