Two ways currently:
Right click their map icon and select "Get Quests". Now open the quest window and the "Player" tab should be selected. That grabs the current status of all their quests. Crude, but it works.
Look at their map icon tooltip. It will show the current tracked quest or the last one an objective completed for.
Adding their quests into the watch list is on the short todo list. Meaning it will be done in one of the next few versions.