My sister bought me a cast iron ebelskiver pan, and I've not had much luck with each of the batches I've tried. They always burn or stick.
I'm hopeful someone might have a tried-and-true technique for making them, and possibly a family recipe :)
There are a number of things that you may or may not be doing that is causing the problem, so any of the following "solutions" may fix it for you. I am basing this on "burn" and "stick".
4 is probably the most important, since burning will mess up the oily patina you are trying to build up on your pan. The others will all help. As I noted in 1, your pan will improve over a period of time as the surface seasoning improves.
Just to add on to the above answer (which is spot on):
Add an oil coating after your pan has heated to cooking temperature completely, just before you add batter. The heat tends to allow the oil to coat more evenly and you'll need less oil overall to create a completely non-stick surface.
Other than that, the more you use that pan, the better it will be as a cooking surface. Don't begrudge it a screw up every now and then, even the things it burns makes it better.
Regarding recipies, try throwing this one through Google Translate and pick any of the recipies you like: http://www.dk-kogebogen.dk/opskrifter/retter-3.php?id=482
These are Danish recipies, and I believe ebelskivers (æbleskiver) to be a Danish thing.
Have fun :)