I'm not saying I'm Jesus, that's for others to decide.
I maintain that if you want to kill someone and don't want to get caught, then it has to be a homeless person, living no less than 5 miles from your home, but no more than 20.
You have to walk up to them, briskly, late at night and then suddenly reach out and stab them in the chest, as close to the heart as possible. It'd be good to be wearing a long coat that masks your body shape, and a hat would be handy too.
Walk away, knife still in hand(or, by now, pocket) and hide in the shadows of an alley or doorway for a good half an hour, maybe smoke a cigarette and look at your watch impatiently, then stride off 'annoyed'. When the police look at the surveilance tapes of the area, you need to be either not visible or not acting like someone guilty. A guilty person would leave the scene obviously and quickly. Keep your cool, look normal.
When you get home, wash the knife thoroughly, and put it back with your other utensils. The police aren't going to be able to use it as evidence if it isn't near the scene. If there is any blood spatter on your clothes, bleach them. It doesn't matter if they get irrevocably coloured white - you need to get the evidence off.
In the next few days, don't even think about what you've done. Treat it like a mundane, everyday task. It's done now, we can leave it be. If you think about it, you're going to end up giving yourself away, by either being tempted to revisit the scene, or by reacting suspicously when someone mentions the news story to you.
You must wait at least a year before the next time, but it can't be a year exactly, or they'll immediately think you're a serial killer working with a pattern and they will profile you like *that*.
Never tell anyone what you did. Don't even think about it too often, or you will f*ck up.
And that's how you murder someone.