Translation:Show me how Skype works please.
Why is the word "Skype" here? Is it so immensly popular in Ukraine that it's synonymous to "online messenger"?
Skype is popular throughout the world not just Ukraine. If you're learning languages or simply need to talk to friends or family in different countries it's simply a must.
One might say so, yes. It is not as popular as using Google for web search (googling), but Skype is what most people use for video chatting or to keep in touch with their friends/relatives who are abroad. Skype enjoys such popularity simply because it was the first application featuring free calls over the internet.