No, this puzzle is not sponsored by an eraser manufacturer. It simply involves a little trial and error. Or maybe a lot. So if you're feeling cranky today we suggest that you go watch TV instead.
Down to business … The N, S, E, and W after the number of the clue indicates the direction in which the answer is to be written. N indicates the top of the page, S the bottom; W signifies left and E signifies right—unless you're lying face-up next to the puzzle, in which case W signifies right and E signifies left. (We suggest keeping things simple by not lying face-up next to the puzzle.)
The next complication is that after you fill in one square in the specified direction, the word may turn at the first available open square. So you'll have to begin by filling in a couple of answers and determining whether they may cross or overlap by one or more letters. If they do, work from there—but later answers may necessitate some rearranging of your early ones.
It will help to know that the numbers following the clues tell you how many letters are in the answers.