Some folks twirl the spaghetti in a spoon, but often end up with too big a bite. Some simply cut up the spaghetti with a knife and try to eat these bite sized pieces (usually not with much success).
Some simply use a different pasta - rotini, shells, penne, that fit on a fork better.
If you are committed to spaghetti (or other long pasta), I always just pick up a forkful, put it in my mouth and bite down to cut off the danglers. Not beautiful, but not gross, and it's effective. Absolutely no slurping though.
Eating should be enjoyable and not a harrowing experience worrying about every little thing. Keep the napkin handy.