First thing is to be sure you understand the structure of the poem. I've included a link to the enotes study guide on "Ancient Mariner" that will definitely help you. Knowing that the mariner is telling a story to a wedding guest about a journey he has taken to the South Pole, which is the bulk of the poem, and then is destined to find individuals to continue telling his tale to, is crucial. The journey south is crucial, since this is symbolic of a journey toward the unknown, a place a of magic and dreams, a place of unreality, even Hell, in come cases. So it makes sense that the supernatural elements occur on this journey to the south.
The other thing for you to consider is before writing your response is to choose what supernatural elements you want, then explain their significance. That's an important piece to your prompt: "how they add to the events that take place". Basically, you're explaining what the mariner learns from witnessing these supernatural forces and elements.
So write a topic sentence to your response, introducing the title, the author, and the concept you will be discussing ("supernatural elements"). Then give a quick 1-2 sentence summary of the poem that will get you to a moment where you can explain / describe / quote an example of a supernatural power. In the sentence following your example / quote, then immediately explain its significance (how this affects the mariner or what he learns). To develop your response well, use another, different example of a supernatural element; use a quote from the poem as an example of that element, and then explain, again, how this moment affects the mariner or what he learns from this. The final 1-2 sentences of your paragraph should tie this altogether, coming back to mention the author and what Coleridge's mariner learns from the entire journey and how important these supernatural elements are to his journey.
Possible supernatural ideas: "slimy things did crawl with legs / Upon the slimy sea" (watersnakes and their colors); the crew who drops dead and then return to life; the "seraph-men" who light the way toward the north (angels); the "strange shape" with a woman and DEATH in part III; the constant power of the moon and wind and its effect and descriptions.