You can use Shazam right from the Snapchat app to identify a song you're listening to. You can send it by snap to your friends so that they can listen to it.
Steps

Step 1. Open the Snapchat app
Make sure you are using the latest version available so that you can access the latest options that exist on Snapchat. You can access updates on the App Store (iPhone) or Play Store (Android).
The process for using Shazam is the same for both applications

Step 2. Go to the camera screen if it is not open
Tap the circle at the bottom of the Snapchat screen if you're on the chat page or in the My Story window. You will open the camera screen.

Step 3. Walk around to make sure you can hear the music clearly
Shazam works best when background noise is minimal and the music can be heard clearly.

Step 4. Tap and hold on the screen
For best results, tap the screen when your face is out of the frame. This will prevent inadvertent triggering of lens settings.
You have to do this before you take a snap

Step 5. Keep pressing the screen until it vibrates
Two incomplete rotating circles will appear on the screen, Shazam is looking for what music is playing. It may take a while for Shazam to recognize the song. When Shazam recognizes the song, your phone will vibrate.

Step 6. Press info on that title for more details
The song will open in a smaller version of the Shazam app, allowing you to listen to or purchase the song.

Step 7. Long press the info page for that title
You thus create a snap from the Shazam page of the artist, you can then add drawings, filters as for a normal snap. The person who receives it will be able to listen to the song by clicking on the Listen button.