The privacy setting for the activity prevents anyone from being able to see the data, so the share button has been disabled. For the Share button to be enabled, you must set the activity privacy setting to allow Everyone access.
If you look left of the Share button, you will see a group of five icons (pencil, trash can, usually a lock, a star, and a trophy). If you click the middle icon (it may look like a lock, the head and shoulders of two people, or the head and shoulders of three people), you will get a popup that allows you to change the privacy setting for the activity.
There is a setting that allows you to change the default privacy setting for all new activities. If you find that you frequently want to share your activities to people that aren't on Garmin Connect, you might want to consider changing it.
