Wet spots on the grass are very common on LI.  It could be an easy fix or difficult one depending on the circumstances, first make sure it isn't a broken sprinkler head or other plumbing issue, if it is a clay spot it can be fixed by conditioning the soil over time with Gypsum and lime, or drainage could be added with a simple 9” X 9” box or a more expensive and complicated drywell system depending on the severity of the situation.  A bad clay spot will never feel completely dry.