Eels are very easy to catch.
Berley a spot with a few rotten eggs and maybe a rabbit skin tied to the end of a rope. Anything with a bit of meat on works well. Even fish heads.
Leave for 5-10 minutes, then return with a bit of meat tied to a piece of string (wrap in bait elastic bag helps) (again a rabbit skin works well here). Throw the meat into the feeding frenzy and wait for a eel to grab hold and start twisting before pulling it out. Probably 75% would release before reaching the bank but a few would hang on or get caught teeth. This method is much more fun and less messy then removing a hook from a eel.
Under my bridge at home I can even hand feed the eels after a few minutes of Berley. I use to spear heaps but now I am quite fond of the slimy worms.
The very big eels are LongFin eels and are a endangered species. They have the same threaten status as the Kiwi. The smaller or shortfin eels are much more common. Remember that eels only spawn once in their life, while the size limit for most marine fish mean they are large enough to have spawned atleast a couple of times before being kept.