As a Turkish citizen, I have the right to stay in Kosovo 90 days without a visa. But how do I enter the Kosovo at first? What documents do I need besides passport?
When Kosovo grants Turkish citizens visa-free entry for short stays, it is a sign that they don't plan to subject most entering Turks to greater scrutiny than what can reasonably be done on the fly at the border checkpoint.
This has to mean that they don't routinely demand extensive paperwork such as letters of invitation -- if they did, there would be a visa requirement so they had a chance to get a good look at it in peace and quiet.
So unless you arouse more suspicion in the border guard than most other Turks do, what you will need is just your passport, and convincing answers to standard questions: What is the purpose of your trip? Where will you stay? When and how will you leave Kosovo again? Be prepared to document your accommodation bookings, tickets for the journey back home, and that you have enough money for your expenses during the trip.
(if you think you do look suspicious, arm yourself with as much documentation as you can lay your hand on, and hope for the best).