Depends how you want to share your playlist - if you want to just send it to someone else to play right click the playlist and copy the address to the clipboard. The address can either be a URL for use in a normal browser or a URI which works in the Spotify client.
e.g
http://open.spotify.com/user/atitlan/playlist/0TQGMBokKlk9KJG3lyDGGt
or
spotify:user:atitlan: playlist:0TQGMBokKlk9KJG3lyDGGt
If you want others to be able to add stuff to one of your playlists mark it as collaborative and then send the link onto whoever you want to access it (I think).
For fellow last.fm users, it would seem that Spotify view their service as complimentary to last.fm as you can scrobble directly from the Spotify client, just set your user and password in preferences.