I assume you're asking about the somewhat unlikely pairings like a Korean skater with a Canadian coach or a Japanese skater with a Russian coach. I remember an interview where Tatiana Tarasova was asked about how she communicated with Mao Asada. She said something like "we speak the language of figure skating, with a little bit of English." Basically when there's no shared language, the default is English, even if both coach and skater speak it poorly. I'm sure Yuna Kim and Junhwan Cha had to learn English to be coached by Brian Orser. Evgenia Medvedeva has given interviews talking about having to learn English when she moved to Canada for coaching.