The G-Man coming nearer and says: It’s those time again To join and serve! So Rise and Shine Mister Freeman!
If I was Gaben I would come to some game convention and present more stuff about Source 2, at the end of presentation and before leaving from stage I would say:
“Oh by the way Half Life 3 is in develoment, good bye” and walked of the stage just like that 
Well, I’d simply do something pretty damn basic.
Release it on Steam on sale, then wait for the people to play it and say how awesome it is.
And that’s it 
.
Ask the RL one
I would do it how Bethesda did Fallout 4. Start a countdown timer with a faded Lambda symbol in the back and a clearly visible crowbar. The countdown would be in days, hours, and seconds and it would NOT be “Valve time.” When it’s over, start the most epic trailer the world will ever see. I would probably have it be Alyx giving a monologue on the previous events so that we’re all caught up and keeps us waiting in great anticipation.
Unintentionally, via the unavoidable leak that I bought the IP from Valve.
Intentionally, but releasing a trailer when it’s ready to launch.
Mysterious middle aged men in business suits, carrying black briefcases with the lambda logo clearly visible (or just the number 3), would start to appear in various locations around the world.
Release it on steam, not tell anyone and see how long until people find out about it.
A month before release perhaps (without being announced) they start putting on sales for every Half-Life Game - at $3 - starting from HL1 till EP2. And then on the last day, they release a teaser - very vague, and at the end, a 24 hour countdown with the lambda symbol in the background.
Half-Life 2 Episode 3 and Half-Life 2 Episode 4 Return To The Ravenholm as playable gameplay.
I would start with a very complex ARG, that the final end result has nothing to do with half life. After that, “accidental” leaks would happen. We would talk about Ricochet 2, portal and left 4 dead. I would hint at a new upcoming game. Another, more complex ARG. Final result is a picture of a briefcase. And finally, after two years of this, i would go to E3, talk about VR, steam machines, and the VIVE headset. Before i walk offstage, I would say" Oh, and also, Half-Life 3 was released for free on steam today. Only people who downloaded it during this conference will get it for free. For everybody else, 60 bucks. Deal with it." and then i would walk off stage.
To meet Gabe Newell(Half-Life 2 Episode 3) and chairman of Arkane Studios(…Return To The Ravenholm) I’d like to mention rumour why Gabe can’t count to 3?Because of that he didn’t make Windows 3.0(Half-Life 3)?
What did you just even say? You do know that ‘Return to Ravenholm’ was never even close to completion? And what are you on about with Windows 3.0? You think Gabe was in control of Windows development at that time?
Oh god…
Well, you’d have to do it at E3, of that there’s no doubt. Here’s how I’d have it go down: there’d be a fairly standard preamble about showing a trailer for their next project, no hint at all they’re finally dropping the bomb. Then, the lights would dim, and for a moment, there would be nothing but a black screen.
Then…
“Dr. Freeemaaaan…”
cue Half-Life logo with a ‘3’ in it.
Then there’d be a little speech by the G-man with at least one line about how 'you’ve been on quite the little…vacation, haven’t you?" or something like that.
I would probably do it with a countdown, but the website the countdown is on has a URL like “half-life-3-the-game.ru” or something along those lines (you know, so that it totally sounds fake).
Make the Lambda Logo on the countdown page really badly photoshopped and make it look really amateurish in general.
People will quickly just call it an obviously bad troll and move on. But then, when the countdown is at 0, the most epic trailer in the history of gaming is being played and game activation codes for Half-Life 3 are being displayed, but only temporarily to reward those who have been waiting for the countdown to reach 0.
How would I announce Half-Life 3?
Very, very carefully.
Through ARG, leaving it to us to find and unlock episode 3 , which would be tied to the xen update, also with the rest of the games in the Half-life and Portal games. Important info in each game that would lead you to a solution for a puzzle in another game. Bringing together the alternate time lines, episode 3 ending with a Gordon lost in time and space, to get the fans rabid for official Half-life 3.
decoding an ip address for us to log into, and unlock the hidden content. Perhaps big brother is lying to us, they say its not there…But it is, trust nobody, with it not being safe, we have to find it for ourselves, working together in unison to defeat BB and the ones that watch.