The way you show someone being shot in your film is greatly dependent on the style of the film.
Old film noir films for example, often showed a gun going off in one shot, smoke rising, and the victim falling to the ground in the next. Or even their shadow!
If you want something that leaves less to the imagination, you could try several techniques.
The first is to position the victim with their back to the camera, have the shooter fire the gun facing camera, and have the victim turn round in pain, clutching their belly, bloody pouring out – blood which you gave the actor to hold carefully just before you shouted “action” [condoms full of fake blood are good here – Ed].
A more gory way of using this technique is to do exactly the same, but have an “exit wound” appear on the back of the victim’s shirt, so it looks like the bullet has passed straight through him. This requires a squib or similar technique to create a hole and a lot of fake blood stored in a baggie, and a great sense of timing, so be careful, and read the notes about using squibs elsewhere in this site.
If you really want to go for it, you can reverse the shot and have the victim getting hit square in the chest right before your eyes. Again, a squib or a baggie full of fake blood and some great timing are in order, plus a good reaction from the victim.
Maybe you could have two men struggling with a gun and it goes off mid-struggle… but you can’t see the wound, or even the gun, until they separate, effecting concealing the actual incident but suggesting it to the audience through sound, reaction and angle.
The more gory you want the shooting to be, the harder it will prove to shoot! You can have armour exploding as a soldier is hit in the chest, which will take a lot of setting up, but even more so if the victim is naked and you want to see the bullet going into the torso, with latex skin and guts everywhere!
And another thing you need to think about is; was that necessary? Is your film a gruesome horror or a Merchant-Ivory film? Are you trying to shock, sadden or entertain your audience?
For a comparison of two ways in which one director showed two different characters getting shot, check out the scene in Indiana Jones and the Last Crusade where Julian Glove shoots Sean Connery; it employs some of the above techniques to shockingly realistic effect! We needed to see Indy’s dad get suddenly and very realistically shot to heighten the shock of the moment, and by God it works. Contrast this with the way Wu Han is shot at the beginning of The Temple of Doom; very stylistic and he barely notices amongst all the noise and popping of corks! Just a quizzical look as he sees a little patch of blood appear on his shirt. Not too realistic, but right for that moment.
So think hard about how the style of the film should dictate the way the shooting happens, and come up with a budgetable shooting scene.
One film my company did involved a girl getting slashed across the face with a knife. We showed the back of the victim, the assailant raising the knife up, the girl throwing her head back, and the next shot was from above, of the girl’s bloody face after we’d put a latex scar and some blood on her face. Got a good audience reaction, and looked very dramatic!