Basically it amounted to myself and about a dozen others, organized into a small chamber orchestra going to Russia for a summer, and in exchange a group of Russians formed into folk/pop entertainment group visiting and staying with us for a while during the school year.
I can't say that 1995 in post-USSR Ekaterinburg was incredibly different than 1991's pre-Russia Sverdlovsk. There were a few bits of free market showing up, but the general economic situation there was pretty dire. Even for me, who grew up in a very rural area and quite poor, felt like I came from nearly unimaginable wealth.
A couple years later the State Department and Russia repeated the exchange and I had a chance to show my host mother around the local shopping malls and such. The "change" from communism had already happened, the Russians by then were by and large waiting for America to arrive.
It was an amazing experience, once in a lifetime, and it has given me lots of both wanderlust and perspective that I've carried with me for the rest of my life. I was very happy to see the improvement in standard of living in many parts of Russia over the years, but I'm very sad to see what they're wasting it on at the moment in Ukraine.