How do I move my contacts onto my sim card without actually being able to see the screen?

I have a Samsung Tocco Lite, which I recently took to Alton Towers and it was subsequently wiped out by the water on the flume ride. The phone still kinda works, the touchscreen and sound still work, but the screen's completely kaput. I've got another phone I can use, but I don't want to lose all my numbers, so if someone can tell me how to move the numbers (and exactly where each of the ons to do so are!) that would be lovely. If anyone can get hold of screenshots, that would be extra lovely.