Dear Emerald Jade,
I must start by congratulating you. You are only the seventy-second to ever successfully deliver a letter to me. Such a high number may make it seem like not much of an achievement, but remember I've been roaming this world for aeons.
Your letter makes me glad. It's solace to see that there are some who don't fear me. Perhaps if others see how amiable I can be, the nearly-universal dread of myself will begin to lift.
On to the purpose of this letter.
First of all, I must say that if you want ponies to think you're dead, the best method is to be dead. But for some reason, the idea of letting mortality run its course is disagreeable. Ponies. Can't let nature be.
I digress. I agreed to give my thoughts on the most effective methods to convince your fellows of your inexistence.
There are two main parts to this practice: inducing the idea of your demise as factual, and keeping it that way.
At first glance, this initial phase is simple. There are many, many ways to die. I of all ponies know this. Frozen in the cold, fallen off a cliff, burned in a house fire. One of my personal favorites is getting poisoned, impaled several times, beaten, and tossed in a river, dying only from suffocation.
The problem is, you don't want to actually die. On top of that, I assume you want to walk away. It's simple to drink a cup of wine, cry poison, and fall over, but you can't just stand up and walk away when nopony’s looking. A moving body is not a dead body.
So, you need to “die” in a manner where the absence of your body is easily explained, or, better yet, expected. For example, you could “drown” in the sea; your body will presumably sink into the depths.
However, there is another way.
You reside in Ponyville, correct? Perhaps you remember an incident some time ago when one particularly lively citizen managed to clone herself several times. She did this utilizing an enchanted spring commonly named the Mirror Pond. It has since been blocked off by a boulder, but this is no obstacle for one with enough determination.
In case you haven't caught on, I am suggesting you use a duplicate to simulate your death. Now, I understand you may have some moral qualms about killing yourself. After all, murder is so much worse than lying. Let me assure you that the clones from the lake have no souls. They are merely empty shells that act and appear as you do. As a matter of fact, your darling budding princess dealt with the above-mentioned crisis by terminating the doppelgangers. If this does not assuage your sense of guilt, keep in mind this is just an extra measure to ensure your feigned misfortune isn't suspected, and not necessary. You'll just have to be clever.
As for the latter half of this whole process, that is, remaining “dead”, you must stay disguised and/or hidden, of course. Simple, I know, but not simple enough to keep me from providing pointers.
You must be completely unrecognizable. Completely. Dye your coat, mane, and tail. Style your mane and tail differently, maybe even cut them. Wear colored contacts. Et cetera, et cetera.
Adopt a dialect other than your own. Drop your mannerisms and create a new persona. Train yourself to respond to whatever new name you give yourself, and completely ignore your old one.
Most importantly: change your cutie mark. Almost every pony in existence has a unique cutie mark. There have been instances of shared cutie marks, but you must not rely on exceptions.
Be sure to make any and all preparations discreet. Make all these changes as permanent as you can or desire. If you pull it off well enough you could even attend your own funeral. With enough preparation you could even write your own obituary.
Having said that, I now recall another point you must consider. Why are you doing this? You did not tell me, and I do not need to know, but you need to know. I ask that you don't go to unnecessary extremes and ruin your life. That's my job.
I wish you the best of luck in your endeavors.
Your faithful reaper,
Death