If you would like to link your Dragon to a Companion, you first must find one. Companions are fairly common in some species. Others are few and far between. Once you do find the perfect Companion for your Dragon, wait until a new Link Moon has entered the sky. At that time, the Ethereals Companion-related magic is strong enough to link Dragons and Companions. When the Link Moon appears, SPO will post on PonyIsland and accept new applications. Links are limited, so get your forms in quickly. You may unlink a Companion at any time by PMing SPO. This is not recomended often on one Companion though, as they will leave you for freedom if they want to.
Some Companions are gifted with magical abilities. How and why are unknown. it is also unknown how the Companions are chosen. Some of the discovered magical abilities are; Granting itemless breeds, always breeding twins, giving a trait to babies the parent does not carry, and changing a marking or mutation. Some magic is endless, like breeding twins. Other magic, like changing markings, is single use only per Dragon.