I would think the best way to get there from the Contemporary is to walk over to the Magic Kingdom entrance, then take the boat over.
We ate there for the first time this past Sept and we really liked it. The food was very good and my kids (4&5) had a fun time. It was definately loud, which is fine by us..but just thought I would mention it. It is not a place that is a 'must do' for us now, but I am glad we tried it once.HTH!