Hm, I don't quite understand how would you like to ask it on Etsy. A contest have nothing to do with Etsy, it should be held on Facebook or other social media, and the only thing you can do here on Etsy is to put a note in your shop's announcement, something like ''From (date) to (date) you can participate in a giveaway on my FB page" or ''Visit my FB page for latest news, discounts and giveaways".
Of course, most people do not read shop's announcements at all, but that's something we all have to get used to. You can't really do anything else here - sending messages to lots of followers is considered spam, so you can just put it in your announcement and 1 in 100 will note it. The others that are going to participate will be the people who liked your FB page before.
