A good hold is the first step towards accurate and safe shooting. Most slingshots are designed with a certain type of holding in mind. Most people hold the slingshot with the "weak hand" that is, a right-handed shooter holds it with the left hand.
This is by far the most common grip for today's slingshots. Just form a tight fist around the handle.
Only very few slingshots, namely the Milbro and the Hy-Power, use this grip. It can still be found some today's boilie catapults and toy slingshots. I doubt you can shoot accurately with this design , but it is possible to make very small pocket slingshots, as the handle can be much smaller. Take care not to hit your finger if you choos this grip!
This is the way to hold classic and "Spain" type slingshots. The index finger wraps a bit around the fork, the thumb supports. It is possible to be very accurate this way. Most profesional shooter use this way when shooting non-wristbraced slingshots. Unfortunately, most of today's commercial slingshots must be held pistol-grip style.
Same as above, but the thumb goes around the fork, too. This is my favourite method of holding.
..they were just too good to discard :-) thanks to Gary for these pictures!