You will need to sand off all of the paint and apply a quality deck stain.  Work on just the floor if it is the only area affected, you can sand off the handrails later if needed.
 
Choose an oil base stain if available in you area, the water based stains have less penetration and can peel instead of fade.  Also, a semi-transparent or semi-solid stain will penetrate more than a solid and have less chance of peeling.