I used to work in this exact field. First of all, there are two copyrights on the song. You will need permission to use both. These are the recording copyright (the recorded version of the song you want to use) and the publishing copyright (lyrics and composition). These are not always owned by the same label.

Find the version you want to use, then find the synchronization or licensing department of the record label that holds each copyright. You'll be able to find a generic email for them via the label's website. They will tell you how much it will cost and provide a license for use of the music, which will only allow you to use it as described (e.g. on a website available in one country, on 10,000 DVDs, etc.). Provide them with as much info as possible, including your budget, what you want to do with it, what format the video will be available in, and what region you want to use the song in.

To complicate it further, labels don't always own a global copyright on recording/publishing. A common split is one label owning North American rights and someone else owning rights for the rest of the world. However, I think you can usually find a lot of this info on Spotify.