The Blue Snake, much like the Red Snake, has a primary purpose of transferring Rings from one game to another. In order to do this, Link must have two Game Boy Colors, a Game Link Cable, and must be playing a Linked Game. It does not matter whether Oracle of Seasons or Oracle of Ages were played first, but it must be a Linked Game in order to transfer Rings. Rings cannot be transferred from Seasons to Seasons or Ages to Ages, as different games must be in each console.
If two Game Boy Colors or a Game Link Cable are not available, Link is not able to use the Blue Snake to transfer Rings. However, Link can still transfer the Rings through the Password system using the Red Snake.
Other than transferring Rings, the Blue Snake can also be used to acquire additional Rings. If two Game Boy Colors are linked with a Game Link Cable and the two players simultaneously speak with the Blue Snake, both players are rewarded with a Seed Ring.
While no specific Rings are exclusively found through a Fortune Link, there are several Rings that are only found by bumping into Maple, inside a Gasha Nut, or through a Fortune Link. The Blue Snake serves as a good way to acquire some of the more common rings.