heart rate zones

To see zones in Garmin Connect, select "head & shoulders" icon, then "settings" then "training zones" then "device settings"

You can only see time in zones if your device has that capability (if it doesn't, the "time in zones" link does not appear in the activities window)

Is there a way to see what your heart rate zones are…

In Garmin Connect online? What mickw46 said, or you can get to the same place via ≡›Devices›User‑Settings (assuming you only have one Garmin device registered against the Garmin Connect account in question).

… and to show them in the graphs of a workout?

That depends on what you mean, and which Garmin device you have. If you have a model that supports the Time in Zone feature, then technically the answer is yes; you can see the range for a particular heart rate zone (as recorded) in a tooltip, when you hover the mouse pointer over its label on the Time in Zones bar chart for an activity.

However, you cannot have (boundaries of) HR zones marked out against the vertical axis on the Heart Rate line graph, or otherwise overlay that graph with horizontal bars to tell you where the zones begin and end, irrespective of whether you're thinking about the settings that were applicable at the time the activity was recorded, or the settings that are current when you review the recorded activity.