I put my ipod nano in Logitech speakers but there no sound . how it work ?

Is the power supply for the speakers connected (if separate), the speakers powered ON, and the volume (on the speakers) turned UP? Do these speakers work for other devices that connect to it in the same way?

Do these speakers connect the "regular" way, using the headphones jack on the iPod. Or are they special "iPod" speakers that connect using the dock connector on iPod?

You can't add any software (apps) to an iPod nano. If you have not already, you can try doing a Reset on the iPod

http://support.apple.com/kb/HT1320

If that does not help, you can do a Restore in iTunes. Select the iPod in the iTunes sidebar, under DEVICES. To the right, on the Summary tab, there is a button for performing a Restore. This will erase the iPod, install the latest software, and set it to default settings.

If that does not help, you should check the specifications for that product to make sure your iPod nano model is supported.

Try the suggestion mentioned in this article - Why won't my iPod play through my iPod speakers or car kit?