How do I get to the desert?

Solution 1:

The Desert is in the South-west corner, as is documented in this wiki article. There is a detailed article as to how exactly to get into the desert. The basic steps are:

1. Try to find Marin. Start in Mabe Village.
2. Head to Toronbo Shores. There after some searching you will find Marin.
3. Head to the desert, and she will sing to the Walrus. That will cause the Walrus to move out of the way, allowing you access to the Desert.

Solution 2:

You have to travel through the Animal Village. Immediately southwest of the Castle and Seashell Mansion, there is a shrub/bush to remove, which reveals a staircase:

Should be straightforward from there:

The animals in town mention needing Marin to wake the walrus blocking the path. Marin is waiting by the ocean, where the story began.

Here is a screenshot of the Game Boy version, per zeldadungeon.net's walkthrough;