You can take the Airtrain from your terminal to either Howard Beach station for the A subway or to Jamaica station for the E subway and LIRR. Airtrain/subway is $7.25, add another $6 or so for LIRR. Depending on where in Manhattan you are going it will take at least one hour or more via subway, faster by LIRR. Go to www.mta.info/nyct for maps and info.
You can take the Airtrain