As event medic at numerous Scottish trail ultra marathon races, I frequently get asked to remove ticks from strangers and friends alike.
One especially memorable occasion was one of our regular female runners, who was insistent that I must carry out the deed for her. The tick had buried itself quite deeply among some quite delicate folds. Needless to say, gloves and head torch were required.
The important skill is in the gentle rotation or twisting of the offending beastie; you are attempting to disengage the barbs around its mouthparts, without squeezing any gut contents into the wound site.