The elbow lever is a position where the body is held
up horizontal to the ground. But unlike the planche (where there is NO
support along the length of the body), the elbow lever uses one's elbows as
a resting and balancing point for the body. This makes the skill much easier
than a planche.
An elbow lever -

It's a fairly simple skill really. There's just several key points in order
to find the correct position.
The Hands
You'll want to put your hands down on the ground about shoulder width apart, with the fingers pointing to the side, or even slightly backwards. This hand orientation is essential in balancing the skill correctly.

The Elbow Stab
What's this about stabbing? Well, as I mentioned before, your body is resting and balancing ON your elbows. In order to do this, you need to learn the correct place to put your elbows. This placement is called "stabbing".

As you can see from the picture above, you'll be placing your elbows to
either side of the middle. The placement of the elbows is fairly intuitive,
as your elbows aren't going to be able to meet in the middle of your body,
and if they are placed any farther out, then your body is not resting on
them.
The picture below shows a single elbow stab into the correct position. Your
elbow should rest right at the edge of your 'six pack'.

If you were to take one arm and stretch it across your body like so, then
you can easily find the correct position. It should feel like your elbow is
sitting into a groove.

Of course, this is also a good stretch to do if you find inflexibility is
making the elbow stab difficult.
You can also work the traditional shoulder stretch to help any flexibility
problems.

When your elbows are stabbed, your arms will be parallel or turned slightly
outwards. If you try this skill on a set of parallettes or rings, your arms
will definitely turn outwards, forming a trapezoid in the empty space.

If you
find your elbows slipping off your stomach, there are two things you can do.
First is to work on your flexibility with the stretches I showed above. The
second is to put your hands slightly farther apart. By doing this, the base
of that trapezoid (space between your hands) is longer and the sides of the
trapezoid (your arms) must lean at a sharper angle in order to meet the top
of the trapezoid (your stomach). The result of all this is that your elbows
are stabbing more toward the center of your body and less likely to "pop"
out. Confused? Good, let's continue.
The Start
With the correct hand orientation, hands about shoulder width apart, you'll want to lean forward and "stab" both your elbows in at the same time.

You should start to feel the support that your elbows will be giving you.
If you are still having problems getting your elbows into position. You can
also hunch your back over. I find this helps in getting the elbows into the
right position.

Whether you start with your body in a straighter position, or hunched over
is unimportant if you can extend into the elbow lever in the end.
The End
After you stab in your elbows, you'll want to ARCH your body to make it more horizontal. This will lift you off the ground and into position.

There are three main points to remember when extending into the elbow lever.
You'll be doing these all at the same time -
1. look upwards - the spine follows
the head, so looking up will flatten your back out.
2. lift up your legs - you'll feel
this in your lower back, as you'll essentially do a reverse hyper extension
of the back. Really work to extend as high as you can. Try not to bend your
knees though.
3. lean forward - you'll have to lean
forward and open the angle of your arms to balance correctly. Elaboration of
this point follows.
oh yeah . . . and don't forget to breathe. I know it's hard, what with your
arms stuck in your gut, but it helps to cut down on the red face.
The Arms and Balancing
The most common mistake regarding the arms and balancing that I see is keeping the arms at a 90 degree angle. This is simply because that arm angle feels more natural when you are pressing something away from you (in this case, the ground).

Doing this will put your body off balance, and your legs will generally rise
upwards as you fight to stay up.

So if you find your face heading toward the ground, like the picture, then
it's often a matter of the angle of your arms.
Instead of a 90 degree angle, lean forward as you straighten your body. Your
arms should be at more of a 135 degree angle, like so.

This will shift your weight and balance you out quite nicely. This is also
why your hands are placed with your fingers facing to the side or slightly
back, as it's not really possible to get your arms to this angle if your
fingers are facing forward. You'd have to fold your wrists over top your
hands.
Supplemental Exercises - ***Revised***
I had previously recommend Supermans (pictured below) as a supplemental exercise for this skill if you had trouble extending your body. While it certainly will help, it's important to note that the exercise will put a great amount of stress on the spine. It should be used cautiously.

Even the reverse hyper-extension, shown here, can be a problem as it causes shear loading of the lower back and can cause back problems in some. Again, feel free to use it, but be aware of the risks it can impose.
A safer alternative recommended by Dr. Stuart McGill is the cable pull-through. This of course can be done with elastic bands as well if you don't have access to a cable stack. This will strengthen up your hip extension and should allow you to hold the elbow lever position easier.
In the
end, feel free to use all or none of these exercises. Simple practice of the
skill, as with most bodyweight skills, will help improve your form as well.
Wrap-Up
The elbow lever is
something that should be practiced in short sessions fairly regularly in
order to learn the correct balancing and placement. Each time you get into
an elbow lever, it'll feel a bit easier.
Here's another picture of an elbow lever I had, so you can see things from
another angle.

You're levering your body on your elbows. Simple enough, eh?
Where to do this. . .
Once you figure out the elbow lever, it's quite a simple move to do just about anywhere you can get your hands down.

For a platform that's a bit above your hips, you can put your hands down,
then hop up and land into the elbow stab.

After you've landed in the stab, then it's just a matter of extending
yourself and straightening out. Of course, make sure you have this skill on
the ground before you start taking it to new heights.
