The first step with Zen is to visit the install where you want to export your content from. Here, you'll be able to pick the elements you want to export, and the date range to include modified elements from. Once selected, this data will be downloaded as a .zip for you to upload when importing on your destination install.
Exports will contain a .json file which is a serialized collection of your content for all elements. It'll also contain any local assets for any asset fields or asset elements. These are so that they can be uploaded along with the asset element itself.
Most elements are grouped in some form. Entries have sections, Categories have groups, Users have groups, etc. When exporting, you can pick all element "groups", or pick just what you need.
For particularly large installs, it might be helpful to select a date range of content to export, rather than export everything. Using the date range controls, this will select only elements whose dateUpdated value falls between the two dates.