Oxidation occurs when environmental exposure dries out the gel coat, causing it to lose both colour and gloss. You should remove the entire dead gel coat before lasting high gloss can be restored.
Lightly oxidized gel coat can be easily restored with a liquid, non-abrasive cleaner/wax such as
Meguiar's® No. 50 Cleaner Wax. Unlike most cleaners, this one-step product cleans chemically without using harsh abrasives. This is the only product a properly maintained gel coat will ever need.
Moderate to heavily oxidized gel coat will require more intense measures. Depending on the severity, the object is to remove the layer of oxidized gel coat, which will require a cleaner or compound. After the oxidation has been removed, follow with a high gloss polish to restore gloss, and then a long-lasting wax to protect the newly restored finish. A simple 3-step system can be found in Meguiar's® Fibreglass Restoration System, which includes a cleaner, polish and wax: