Usually, if you have real good ones, the skin will come off fairly easily. Then, and this needs some dexterity, you'll proceed by pinching and feeling your way to the central bone (eels have only one so that makes it rather easy) and the "feeling" bit comes in because you need to decide which way the spikes go so you can pinch and slide the right way down (imagine stroking a cat against the hairs...). The flesh is firm, very rich and smokey in flavour. We used to eat them like this, old newspapers on the dining table and have an eel fest (mind image: the face of my dear husband seeing these eels.... he really thought eels were born as fillets). Best to serve this lukewarm, I like to leave them on the radiator for a while (wrapped in paper). We eat them as they are, but usually it's served on bits of toast, or as an appetizer on rye bread. Pulsed into a paté mixed with herbs and horse radish is also very good, but somehow we never get to that stage.Resulting bits and pieces of eel meat, I made a mess but the flavour was soooo good!
A word of advice; try to get the skinnier ones, although it might look like a good deal to pick thick eels, these tend to be dry and sometimes taste bland (or muddy). Best size is finger thick. In earlier days my grandma used to make stewed eel from the -untreated and fresh- thicker ones ("Paling in 't groen"). I still remember riding the bike with my grandfather to the fish stall, my feet firmly planted in his bike bags, buying fresh eel. Biking back home with a wriggling bunch of eel rolled in newspaper. Then, I got to sit on the kitchen counter, armed with a large wooden spoon while the eel swam in fresh water (to make sure they were clean inside and out). My job was to push them back in the sink.... Suffice to say I never ate the dish, the memory plus the smell of fish stewed in milk and herbs....no thank you. My oma and mum however thought it was a real treat! Sure!
Edit: my mom read this and told me that the white liquid I remembered seeing in the pan (I think I was only 5 or 6) wasn't milk, it was butter.... 'kay....still not something I'd like to try. Thanks Mom, for helping me out here!