Best way to repaint exterior wood stairs?

Yes- scrap and sand as needed. I would recommend a generous coat of oil base primer, thinned slightly if doesn't seem to be soaking into the wood. This is basically the coat that protects your wood and prevents moisture from entering which will cause peeling in the future. Two coats of a low sheen, high quality exterior latex finish is your best bet. However, give extended drying time between coats and especially after second coat. Oil that I prefer is ready for use when completely dry but latex maintains a soft set even up to days after drying and lends it's self to transference to hard,warm/hot surfaces that come in contact for extended periods of time. examples like work boots, flower pots,toys etc. especially if steps are in a area of extended sun light.