After you have taken all of the medication associated with a particular alarm, as indicated by the blue lights on the pillbox, simply close the lid and you're done. The action of opening and closing of the pillbox, following an alarm, is interpreted as the act of taking your medication. This is apparent upon closing the pillbox, as the blue lights specific to that medication will be cleared. Additionally, the pillbox will log this compliance data, recording that all off the medication for this alarm has been taken successfully.
If you want to skip rather than take your pills, hold the Ellie icon on the lid town for 3-5 seconds without opening the lid and it will track this as "skipped".