This was done in the IS01 (a Japanese android). And my debian GNU/Linux machine.
Obviously the first step is to get the application (apk) file.
In this example I’m using «Piano_Play_7.0.apk», a crappy piano application.
In your android:
Go to Settings -> Application Settings, and «check» Unknown Sources.
Then, in Settings -> Applications Settings -> Development, check USB debug.
With this done, all you need to is get the android’s SDK (linux doesn’t need any extra divers). It’s very small, and brings mostly binary (doesn’t need to install!!) so it’s pretty straight forward.
You’ll get a file like: android-sdk_r07-linux_x86.tgz.tar
So put that in some rational directory, untar it
tar xvf android-sdk_r07-linux_x86.tgz.tar
and
cd android-sdk-linux_x86/tools
From this point you’ll have to become root
su
adb kill-server #in case you tried without being root
sudo adb start-server
adb install /home/myusername/Piano_Play_7.0.apk
If you mounted your device remember to unmount it first.
And then remove the usb cable, and try your new application a try!