Wild camping in Wexford, Ireland

Do you mean the town or the county?  It depends really.

I would not recommend wild camping within a mile or so of the town.  Your best bet would be either going west into the high ground where there are conifer plantations - normally nobody is too bothered about camping in those so long as you don't have an open fire.  There are also extensive dune systems between the town and Rosslare, you can probably camp in a discrete spot among the dunes overnight without a problem, but check the weather forecast as they can be very exposed in high winds.  I've known even very experienced campers get caught out by storms when camping in dune areas in Ireland.

If in the county, you can wild camp pretty much anywhere so long as you ask the landowner.  Its quite an agricultural county so there isn't much spare land, but there are quite a few woodlands and areas of scrub around.  Just knock on the door of the nearest house to ask who to ask for permission.  Its rarely refused, and if it is refused, its usually for a good reason (i.e. the land is used for bulls or horses).