Killing someone is easy. Go buy a gun at Wal-Mart, sit in front their domicile some early morning, and pick them off when they emerge. Groggy with sleep, or focused on their work, they'll have 3 bullets in their chest before they realize they're being shot.
But, that's not the answer you wanted. You wanted to be able to get away with it.
The Hard Part
It is amazingly gratifying to kill your enemy, to see their eyes grasping as life ebbs away. It is also equally gratifying to kill your enemy, and to sleep soundly knowing that you'll never hear anything about it. It's a pity that these two goals are diametrically opposed; the closer you are to the target, the higher your odds of getting caught. There is no balancing of these goals; either you need to see them die (go visit Wal-Mart now), or you will gladly use distance to avoid getting caught.
You have three ways to distance yourself: geography, people, and time. You need to immediately remove yourself from being near the person you're going to kill. If you have a relationship with the person, you need to act like you're patching things up, and then move away. If you can't bear to talk to them again, just leave. Most murders occur "in the heat of the moment", so if the target can push your emotional buttons, Leave!
Honestly, the prospect of moving can be daunting. Don't hesitate to use any means possible to get away. Some people I've talked to have the hardest problem with this. They want to stay put. They think that "things will get better" if they get a new s.o., or just don't talk to them, or whatever. These are the people that either end up living the rest of their lives in fear, or they end up dead.
After you have put some miles between you and the target, you need to make sure that you never talk to them again. They can absolutely not be in your life at all, as you'll probably end up driving back all those miles, and killing them. And then where would you be?
The third element of distance is time. After you have severed all contact with the person and moved away, you need to wait several years. Sicilians are absolutely correct when they say:
To understand how all three of these distancing factors come together to help us get away with murder, we need to understand a little about cops.
Every year in the US, thousands of people are killed by other people. Some of the these killers are caught, but a whole bunch aren't. We want to be in the bunch that aren't.
Cops first look at the crime scene and try to find the red-handed murderer when they are nearby. But, we won't be nearby, as we've already blended into the mass of humanity around us. This will be the hardest part, but we'll be well prepared.
Next, cops will look at who had the motive and opportunity to kill. By waiting, we've allowed time for other people to draw close to the target as we drew away. This sets up plenty of natural decoys who will waste the cops' time, or will look guilty. This is why we want lots of distance. Cops live by the principle of simple answers, but as H. L. Mencken says:
We also know that cops have a budget. They can only afford to spend so much of a detective's time looking for solutions. Which is why cops look for suspects that are near to the target, that's where most killers are. But we're not in that group, and cops don't have unlimited budgets, which means that if we've done our job correctly, we won't even be interviewed.
Completing the Target
You need to wait at least 5 or 6 years before you can kill your target. Enough time must pass to allow any issues you had with the target to fade from the memory of the people around the target. Provided that you haven't ever threatened the target's life. If you have, you need to add on another 5 or 6 years, if you did it verbally. And if you did it in a written fashion, you need to forget about killing the target as written evidence has a nasty habit of staying around long enough for some detective to find.
In the meanwhile, you need to do the following things to prepare:
You're going to need a rifle to kill the target. Rifles are best explained away by hunting every fall for deer. You'll also become very familiar with the notion of killing, and with overcoming the emotions you will feel when you kill. Buy several rifles used from previous owners, that way when you destroy your rifle, it won't be missed.
Finally, if you act like a sociopath, people are much more likely to recommend you to the police than if you're a good, upstanding citizen with no criminal record since you moved. Keep working jobs until you find a job you can stand. Try to find someone who can put up with you, and who you can put up with.
After you've done all this, take your normal vacation alone to go hunting. Buy a cup of good coffee and put it in a commuter's mug. Drive to where your target lives, and wait there until they appear after they wake up. Shoot them with the rifle 3 times from a hidden position. Break your rifle down, clean the barrel, put it all in a bag, and walk calmly back to your car. Drive away at a normal pace, and enjoy your coffee.
A lot of people seem to think that "murder in self-defense" is a perfectly good way to arrange someone's death. I'll just remind those people that they are not trained killers, and yes, size does matter. For every single Hollywood showdown where the small person beats the big person, there are at least a thousand dead small people. Not your best odds.