I want to use the song Dirty Diana covered buy The Weeknd for a short film with no lucrative purpose. Do I still need to get the rights and if so how can I do it?
Yes. You need to get the rights.
There is a right to produce a cover of a song for a statutory royalty and, for example, sell copies of the song and play it on the radio. These are called the "little rights".
There is not a right to use a song in a TV show or film without permission from the copyright holder. These are called the "big rights" and must be individually negotiated with the holder of the copyright.
You would need to identify who holds the copyright (which can be done by inspection of the recordings for sale at a store, for example) and then you would need to contact them asking for a license to use the copyrighted material.
Generally, using an entire song in a film, even if it is not intended to make much money, is not fair use.