Venice airport is small, has only one terminal, two baggage carousels and
just a few check-in desks. On the other hand it's friendly enough and it
has a full range of services for travellers.
There is public bus transport from the airport to both the bus terminal in
piazzale Roma in Venice (island) and the railway station in Mestre
(mainland) if you need to go anywhere else. There is a boat service across
the lagoon to St.Mark's, but I think it's a little expensive. There are of
course taxis and water-taxis.