Naples Capodichino International Airport (NAP) is the closest airport to Positano, located about 1h30m by car. Alternatively, you can fly into Roma Ciampino (CIA) or Roma Fiumicino (FCO) airports, which may be easier options for direct flights to and from the US or if you plan to spend a few nights in Rome prior to or after the wedding.
For those flying into Rome airport, a high speed train followed by a taxi or ferry into Positano is another way to reach the destination (we have done this before and it is quite easy).