I think the internet gradually came into common use. I don't think there was a 'launch date,' especially considering no one owns the internet. Launch dates are more or less publicity stunts.
I worked in data processing when I was 18, 1988.. most my time was spent under a compture room floor running cables to mainframes.. WWW was not a common phrase.. In 1994 I rejoined the firm and WWW was common.. I remember when I was a kid working there and these old dudes in their 60's talking computer lingo, it was weird... I took my crawling skills to another place after.. Dumb now I think about it cause computers are a big deal..
I guess that would probably be whenever the first dial-up modem was used to send information through the phone lines. The internet didn't start out as a vast network of people and information spanning the globe. At first it was probably just some companies using the phone lines to transmit business data much faster than through the mail or trying to say it all into a telephone and have somebody on the other end write it all down.
There wasn't a launch date, afaik, it was a gradual interconnection of individual systems. Computers have been using phonelines to transfer data to each other since the 1960's. Back in the 80's there were BBS's that one could dial up but was not connected to anything else. Was basically in the early 90's when all these different systems started to all get connected.
I heard it basically started out with the government and military, as a means of communications in national emergencies (ARPANET). Then universities began using it to communicate back and forth. Then in the '80's commercial internet providers got into the act, and in the early '90's it really took off. I can't find a specific start date for this, but according to Wicki: "The spread of internetworking began to form into the idea of a global network that would be called the Internet, based on standardized protocols officially implemented in 1982."