Hanging off the hoop by your elbows is mostly an exercise in pain tolerance. If you can hang off by your hands (or single hand if trying single elbow hang), you probably have the base strength required.
You can practice this from the floor on any kind of bar. Face the bar as if your were about to do a side mount and hook your elbows on, one from each side. Then lift your feet – you can arch back to look pretty. Here’s a quick example that then moves into single elbow hang:
There is a another position that can be called elbow hang. That is more commonly performed on the top bar. From seated, hook your elbows over the top bar, both arms going the same way. The hoop will need to be the right size for your height, or preferably on the smaller side, otherwise this is nearly impossible. Once hooked, slide your seat off so you’re hanging. To come out, you can slide the hoop from elbows to hands, but it is a bit tricky. See these pictures I found on the internet for an example.
Get used to hanging off both elbows before trying single. When you start learning single, it can help to grab a hold off something, for example your feet into a kind of split. That can help lock you in place. Here are some examples of poses that use that technique, or a leg/foot in the hoop to take some weight off.
In general, experiment a bit with where exactly you’re placing the bar and the angle your arms are at (is the bar right in the crook of the elbow, slightly to the side, etc.). Even moving small amounts can make a significant difference in the level of discomfort.
Some people practice with elbow protectors until they get used to the feeling. That might be worth trying when you’re starting out, or even just wearing a couple of layers of clothes can help with padding.