Download the latest verion of the plugin at: download. There you will see all the versions of the latest release. This release is the development version. if you want to have the stable version then click on Plugingooglemap.There can you select previous releases. If you select one release below the development version then you can download the latest stable version.
Always take the one with the highest character for the latest version.

The file with J15 in the name is for Joomla 1.5.x without legacy plugin enabled. The file without J15 in the name is for Joomla 1.0.x.

To upgrade you need to open the configuration of the plugin in a seperate window/tab. Then uninstall the plugin in a different window/tab and install the new version. Then compare the old configuration in the seperate tab with then new configuration to make it the same.

Alternatively you can use: Intellispire Software Updater for Joomla!