At the bottom of a PM, you can select that you'd like it to be saved in your sent items, but by default sent messages are not saved.
You can change the settings to save sent messages in the Sent Items folder by default...
Open your profile and click the Edit Profile button (it's a button that looks like a crayon at 45 degrees). This will open a page with a raft of settings, as well as your personal details. One of the options is "Save a copy of sent messages in my Sent Items folder by default".
Cheers,
Tom