How did he do that?
The comedians Bud Abbot and Lou Costello performed the bottle and glass trick, known among magicians as the Passe-Passe Bottles, live on TV on the 1950's Colgate Comedy Hour.
Most competent magicians will tell you that it's not the magic trick that's important, but the presentation, and these guys prove that's true. In fact, even though they exposed the "real" method of the trick, it's still being performed today.
A comedy magic act by Abbott and Costello
Here's an earlier version of the same routine, this time from their 1944 movie Lost in a Harem.
Abbott and Costello in "Lost in a Harem"
This trick was old even when those guys were performing it. The trick was fully explained in the book Modern Magic: A Practical Treatise on the Art of Conjuring, by Professor Hoffmann, published in 1876. Here's a set of the bottles and covers from the 1880s:
The Passe-Passe Trick
Other versions of the trick have the bottles multiplying. See this post (the bottle trick is the last video): Magician Tommy Cooper won by failing>>