If you "know" the names of the albums you can make static links using the form http://domain/zenphoto folder/graphics/birds and http://domain/zenphoto folder/graphics/fishes (This assumes mod_rewrite is enabled for your site.)
If you need to discover the subalbums you can use the object model: $mainAlbumObject->getAlbums(0); This will return, in the case of your example, an array containing [birds, fishes] You create the links from there.
The $_zp_current_album variable containing the object of the current album is only setup in album context. (next_album loop or on album.php). To use a specific album outside of that you have to setup the album object before hand. Please take the time to read a little on the theming tutorial and the object model tutorial.
You will probably also need to understand the concept of object orientation.