There is little boat AUL which runs daily between mainland and island. Look the picture...It's small boat so if you plan to go there with car...no way...you have to leave car to the harbour.
Actually there is no point to take car into the island as it is so small.
I found website with the boat's timetable : http://www.tostamaa.ee/client/default.asp?wa_id=178&wa_object_id=1&wa_id_key=
I went there with naturelovers group and they arranged the transport but there is Bus stop
at the Munalaiu harbour ( harbour in the mainland ), so there must be bus connection from Pärnu in there.
I found two buses but there might be some minibus connection too:
Maybe Pärnu's Touristinformation can help you out as well
In winter, when the sea is frozen and iceroad for car's is open you can walk over the sea.
Our group did.
It is quite an experience !