If the points are a dull slate color and if wear is not excessive they can be cleaned with a point file and reinstalled. Don't use sandpaper or emery cloth as this will scratch the point surface and leave small grit particles imbedded in the points. Use a clean file as this will remove a small layer of metal creating a good flat surface to fire against. If the points are burned or pitted they need to be replaced. Also check the coil polarity.
Most engines have a wire running from the negative terminal of the coil to the distributor.
It is common practice to replace the condensor when the points are replaced. Reinstall the refurbished or new point set in the distributor. Rotate the shaft so the cam lobe separates the points, creating a gap, and measure the gap opening with a wire type feeler gauge. Set to specs and tighten the mounting screws. Make sure and keep the rubbing block lubricated with a small dab of high temperature grease.