When a standard headphone or audio accessory is connected, you can initiate audio playback by simply switching the iPod shuffle to the "play in order" or "shuffle" position from the "OFF" position. The iPod shuffle should be in the OFF position for at least 3 seconds before switching it back on. The iPod shuffle will resume playback of the content that was previously being played at a fixed volume level and cannot be adjusted from the iPod itself.

If the iPod shuffle is connected to an external speakers or a car stereo, volume adjustment may be possible from those devices. The iPod shuffle will pause audio playback when the unit is switched off or when the audio accessory is disconnected.

As far as using the remote on the new iPod, the buttons on the remote are used to control audio volume and playback of content. Refer to this document to learn more about using the Apple Earphones with Remote with the new iPod shuffle (3rd generation).

{Source: Apple Technical Articles}