Publishing assets is simple, and there are several ways you can do this.

Directly from the Asset Detail page: simply click on the orange drop down button and select Publish this asset option. This will open the asset in the Publishing tool.

The second way is to select the assets you want to publish. the click the Publish button in the top right of the screen.

Finally, you can also upload assets directly from the Publishing composer. Click the drop down menu Browse files and select the Upload from library option.