You can't really upload tracks, as in upload to the cloud. You can only import tracks into the client so that you don't need another media player to play them.
As I have always understood it, your local music collection is included in the client. If you share playlists containing tracks from your local collection. But if they are not provided by Spotify, friends need to have the same tracks locally as well to be able to play them.
You have to manually import the tracks in both the client on your home computer and in the client on your phone. Spotify doesn't provide any upload / cloud functionality.
I have loaded several track to Spotify on my PC, and can listen to them using the client on my phone without having to manually load/import them there. They sync automatically when you connect.
Further: if the track is in the GraceNote database, you can share the track (via a playlist) with friends on Spotify.