*Arrow, two 'R's.

And there are several ways of doing it. Some work better than others, but here they are:

#1, Cheat using quick cuts, blurred actions, and quick movements:
Show a cut of the guy with an unaltered bow and arrow piece about to let it go, and then split the firing noise between the end of that clip, and one of the arrow flying through the air. Then, you can cut again to the victim falling over with it in his chest.

You can also do a modified version of this by placing the camera so the guy's body shields the bow string from view, when he releases the arrow, have the camera pan quickly staying even with the fast moving arrow. Panning quick enough, and adding a bit of motion blur should conceal the truth that the srting never moves, and the arrow is molded into place.

#2, CGI/Image manipulation using normal parts:
Unless done well, this looks obviously fake. It's where you pretty much erase certain parts of the bow in post, or simply shift the elements into the places that you want them to go. When the arrow fires, you bend the string into a straight position, and move the arrow part forward out of the frame.

#3, CGI using modded parts:
If you cut out the string and arrow out of the molded part, you can add them back in come post-production time. You can then get a more natural look to both the string and arrow, but it requires more advanced GCI, and cutting or Lego parts.

Also, check the animation challenge thread. I believe that shooting a bow/crossbow has been done. And you can probably watch those entries for ideas. I would link you to some examples, but my internet is super-slow right now, so I'll leave the searching to you.

Oh, I just remembered I made this short which is a great example of how to "cheat," as Pritchard puts it.