Like Neuschwanstein also the beautiful castle Linderhof was planned by King Ludwig the second. Both, the castle and the garden can be visited. While the castle building and the grotto (both with guided tour) need to be paid, the garden and the other buildings in it are free to be visited.
Coming to the castle area you need to purchase a ticket already at the entrance to the park, not at the castle or Grotto itself in case you plan a guided tour to one of them!
My plan for the time at Linderhof were to have a look at the castle from outside and the park. I had plans to continue my trip pretty soon and therefore avoided the queue at the castle. Anyway, you should take the tour through the castle. It looks really pretty.
For a little history and some information on the castle have a look at the
official page from the Bavarian Palace Department of the State of Bavaria. It is also availabe in English and very helpful regarding information on ongoing restauration work.