In order to get to Lunar Isle, you would have to teleport to Lumbridge and talk to Lumbridge Sage. When you click on Lumbridge Sage and click "Could you take me to Lunar Isle".

How to get there

Once at lunar isle, head south-east until you see a lunar altar. By south east, i mean; first when you teleport to lunar isle, head east, past the gates and Once there,go south-east until you see the altar.Lunar spellbook is very popular due to the Cure me spell and Vengeance spells.

Switching Spellbooks

In order to change your spellbook you must go to Lumbridge and talk to Lumbridge Sage and go to the teleports that fits your magic needs.