Was it similar to (or different from) how the American media covered the Soviet invasion of Afghanistan?
You can't edit the title, but I do realize that it should be "... cover the Vietnam War?" Sorry about that.
This is a really interesting question. Since this post has been here for 12 hours and hasn't gotten a response, I'd like to chime in. Sadly, I don't think you'll be able to get much information on this subject, unless you can read Russian. If you can read russian, your best bet is to search for Pravda articles from that time period. Most have not been made available online, and few, if any, have been translated into English.
You can find a lot on Soviet foreign policy towards the Vietnam War, and how that intersected with relations towards the United States, but it probably won't delve into the everyday media coverage. (Ex: Ilya V. Gaiduk's The Soviet Union and the Vietnam War).
Hope that helps a little and doesn't count as speculation.