I am not sure what you mean. What type of phone do you have?
You should be able to download and use the Spotify app on your phone (available from google play or m.spotify.com) and log in using the same details as you use on the desktop (requires premium). Your playlists should be there waiting for you. If you have any local tracks which are stored in your computer you wish to transfer, you can do that by following the instructions here.