This video demonstrates how to fix / adjust / repair the timing of the hook on a sewing machine. If the thread from your needle isn't getting caught by the hook that rotates around, this video explains what to adjust to fix that. Requires some very basic tools and takes 15-30 minutes - maybe less.

Thanks to Nigel Chapman for this helpful comment about the timing:
"when you are timing these singer machines there are timing lines on the needle bar to help you get the exact timing required. When the needle bar is at the lowest position you will see two lines: one to mark the lowest point and then the other is used when the needle bar is on its rise. You stop on the second line then adjust the hook to the point where you stopped the needle. Then you should have perfect timing without guessing."