I have a special tool to remove ticks, from humans, but it should work with an animal, too. It grabs the tick very close to the skin, and then you gently pull it out, with a slight twisting and turning of the tool.
Make sure the head comes out, you can see it with a magnifying glass.
Do not try to suffocate a tick, or put any substances like alcohol on it. It will make it get stressed and it will pump more saliva into the animal or human. In the saliva there are sometimes bacteria that can cause Lyme disease. It causes big problems in humans, but I have also heard of cases where dogs caught it. So it is possible that most mammals get it. The normal host is a deer.