Nowadays, the common recommendation is to carefully pull it out.
See
American Academy of Family Physicians:
The most commonly recommended and successful tick-removal method is manual extraction of the tick.7,8,10,11,16,18-21 [Reference 16--Evidence level B, nonrandomized study] A blunt, medium-tipped, angled forceps offers the best results, using the method shown in Figure 1.
I saw on
OSU's site what seemed a good suggestion:
Keep the tick alive for a month in case symptoms of a tick-borne disease develop. Place it in a labeled (date, patient), sealed bag or vial with a lightly moistened paper towel then store at refrigerator temperature.