Why was Ryuk tied to Light's Death Note? In How to Use: XIII, in the second point it says


  The god of Death always remains with the owner of the Death Note.


indicating that a Shinigami will remain with the owner of their Death Note, Light learns this and gathers a group of friends to try and hide himself with Ryuk following him when Misa is trying to find him (she finds him because of her Eyes)

However, the Death Note Light had in the beginning isn't Ryuk's but Sidoh's which Ryuk stole, and unlike Gelus who died and Rem probably obtained ownership of Gelus's Death Note afterwards, Sidoh was still alive so even if Light became the owner after Ryuk dropped it in the human world, the Shinigami who was supposed to be with like was Sidoh.

Also in How to Use 2, the second point says


  The owner of the note can recognize the image and voice of the original owner, i.e. a god of death. 


So is there an explanation as to how Ryuk was tied with Light's Death Note having stolen it from Sidoh?
According to How to use II:


  The owner of the note can recognize the image and voice of the original owner, i.e. a god of death.


Therefore the only explanation for Light being able to see Ryuk would be, that Ryuk is the original owner. But how did Ryuk become the owner of Sidoh's Death Note? As I explained at How did Ryuk trick the King of Death Gods?, it is because of How to Use XII:


  If you lose the Death Note or have it stolen, you will lose its ownership unless you retrieve it within 490 days.


Ryuk became owner of Sidoh's Death Note because of this rule. It wasn't until chapter 65 that Sidoh realized that he had lost his Death Note, which is 6 years after Ryuk first dropped the Death Note down to earth. If it took him at least 6 years to realize he had lost his Death Note, it would be safe to assume that Ryuk had already found the Death Note 490 days before he dropped it down to earth, claiming ownership and becoming tied to that particular Death Note.