Ephemerides for comets and minor planets can be obtained by means of the search engines, or by selecting an object (or an orbit) from some of the lists available in the website. Search engines work by name or designation (IAU designations are used). For numbered minor planets, it is important to put the name inside parentheses.
By default, ephemerides are tabulated for a time interval near the epoch of the orbital elements. If the epoch is close to present date, the ephemeris interval starts a few weeks ago, and spans several months, though this depends on the chosen step increment (default is 5 days). You can produce a new ephemeris by chosing a new step increment, another set of orbital elements, or different photometric parameters. When choosing an orbit, pay attention to the epoch: many orbits have epochs in the past, and if you choose one of those, will obtain an ephemeris for such dates. This means that you can get ephemerides for historic great comets (try, for example, "1760 A1" or "1882 R1").
Orbital elements are constantly updated, so if you save a bookmark on an ephemeris page and revisit it a few weeks later, the requested orbital elements may no longer exist (this applies only in case you requested a specific element set when creating the ephemeris), or perhaps the designation has been superseded. In the former case, the system will provide a new link where you can obtain newer ephemerides.
Every ephemeris contains a reference showing the origin of the orbital elements. Generally, a reference starts with a few letters (that specify the reference type) followed by a number (examples: "MPC 63139", "NC0701"). When this explanation was last updated, these were the references of the orbits available in the Astronomia.org database: