Buy ten bucks worth of Skype credit.
That’s it. Problem solved. Sure, there are tons of “free” ways to get around the ads, but all the ones I tried or read about either broke some of Skype’s functionality or blocked the ads without removing the box that contains the ads: you’re left with a large, awkward, and almost empty placeholder area that says, simply, “advertisement”. Close, but no cigar.
The only reason I’m writing up this post is because it wasn’t at all clear to me whether buying a small amount of Skype credit would - in fact - remove the ads from the app. The last thing I wanted was to spend the money, still get ads pumped into my app, and then have to fight for a refund. But the other day I found this forum post which indicated pretty definitively that all I needed was SOME money on my account to remove the ads. So I took the plunge, bought $10 worth of Skype credit, and - voila! - no more ads. My Skype user happiness quotient instantly quadrupled.
So anyway, if you’re in the same predicament as I was, go ahead and buy some Skype credit. Doing so will definitely remove the ads.