That's a great question!
You have two options: Dear Elder or Pouch. For Dear Elder, simply go to dearelder.com, select the Chile Santiago West Mission (FREE) from the drop menu, click Write a Letter, and fill in Elder Michael Cloward, plus your own address information, at the top. Then write in the text box and click Send Letter when you're done. It should get to him in 10-14 days.
For Pouch, the rules are very strict, but it's the best way to get a handwritten letter down to Chile. Simply write your letter on ONE side of a sheet of paper, fold that paper three times, tape the TOP only, and write your return address and his address on it. Then attach a 42 cent (or whatever it is for normal US mail these days) stamp and send it off. Here's the pouch address:
Elder Michael Bradley Cloward
Chile Santiago West Mission
PO Box 30150
Salt Lake City, UT 84130
In case you're wondering why you are sending a letter to someone in Chile by way of Salt Lake City, these letters are sorted into big bags by mission and sent down from Salt Lake City with whatever general or regional authority is going down there. It's much more secure to send mail to South America this way than to trust the country's mail system.
He leaves in just 2 days, so don't send anything to the MTC at this point. I'm sure he'll love to see mail in Chile just as much as he loved seeing it the MTC!