Your module works on your development site, and its version number in _meta() is the one you want to release. Every update needs a higher version, such as 1.0.0, then 1.0.1, 1.1.0 or 2.0.0. Note the changes in the module's changelog.txt.
In Developer Tools, Global Config, enter:
The Package Module and Package Skin tools appear under Tools once a prefix is set. They only list modules and skins that start with your prefix.
The tool adds the license to the module and names the ZIP after the module and its version. Package Skin does the same for skins.
The xx prefix packages modules for your own sites: install the ZIP on another site to move a module there.
Upload the ZIP to the Marketplace from your profile on jamroom.net. Sites that have the module then see the new version under ACP > Marketplace > System Updates. When they update, the previous version is kept, so they can go back to it.
The jamroom.net upload screens and private release channels aren't covered here. Ask on the forum or contact the Jamroom team if you're releasing for the first time.