To publish a project, you'll need to set an Organization to upload to. If you don't have one, you can make one in the editor or here. Once all is said and done, open up your project settings by clicking Project Settings button under the edit drop-down.
Finally, when you are ready to upload to asset.party, open the edit drop-down and select the Publish Project option
Other than using the Project Settings dialog mentioned above, you can also further manage your project through Asset Party