It'd help if you told us a few things first! Like:
Time period/setting Type of weapon (daggers, "other" weapon, gun at long or short range...) Rank and reason why the person is being assassinated What you're having trouble with
Once you give us a bit more information, it'll help us a lot.
A writer is a world trapped in a person— Victor Hugo
Ink is blood. Paper is bandages. The wounded press books to their heart to know they're not alone.
First of all, think of the motive. This is the most important part. Is your assassin doing it out of revenge? Then make it painful. Is he doing it out of a sense of justice? Quick and clean. Was it spur of the moment? Death by falling over is a good one here, or a quick bash in the head. Never under estimate poison either. You don't even have to be specific, just say "It was super deadly, and practically untraceable." (Not quite like that of course.)
Capture the killers emotion, and the victims fear. It's pretty twisted, but people feel, and you have to let your readers know how they feel. Another great idea is giving your killer an MO, which means Modus Operandi, which means "Mode of Operation".
Make his MO unique, maybe he does two shots to the chest, or always stabs in the heart, something like that. It's like a trademark. He doesn't even have to have an MO, but for assassins and serial killers, I suggest you use one. I hope this helps you out!
Review unto others as you would have others review unto you.
I just wish to note that all murders should be unique. Murder is an art form (in fiction), and should feel, in my opinion, original. Actually, the reaction of the victim can also be very important. After all, it is they who experience the sharp edge of the knife.
