The Skeleton is my very favourite puzzle.
As it is fully symmetrical the first step is to black out all squares corresponding to those shown. (eg if the top corner is blackened, all corners will be blackened)
Every time you find a word, remember to check that the space before the first letter and the space after the last letter are blackened. And again carry this through to all the corresponding spaces.
Check the numbers shown in the grid. Apart from giving you a clue where you are up to in the puzzle, they give you more opportunities for blackening spaces.
For instance, say there is a '15' in one of the squares. Is the clue given for 15a or 15d? If across, obviously the space before is blackened; if down, it will be the space above. By blackening the corresponding spaces all around the grid, you can often tell how many letters your answer will contain. If there is a 15a and a 15d, obviously you blacken both squares.
I always try to match 1a and 1d after filling in what black squares I can. Both words have to start with the same letter and contain the same number of letters.
Don't be scared of Skeletons! With a bit of practice they become a fun challenge. I don't use pencil and have had very little trouble with them. I could spend hours doing Skeletons, whereas I find Acrostics bore me silly!
Good luck with them!