Below is a list of achievements as reported from within the game's 'achievements' screen - I am not sure if this is a fully comprehensive list of achievements or whether there are additional hidden achievements.
There is a page on the Black Mesa: Source wiki, this has now been updated with information on these achievements.
Brownian Motion
Pass the toilet paper to the scientist in need.
Caffeine Extraction
Perform a surgical caffeine extraction from 20 machines. [0/20]
Calculated Trajectory
Kill 10 Airborne Headcrabs using the Shotgun. [0/10]
Centripetal Attraction
Kill 20 enemies with the Hivehand. [0/20]
Convection Refinement
Ruin the microwave casserole.
Dead Reckoning
Kill an Assassin with the 357 Magnum.
Digital Wizardry
Kill 10 enemies with a reprogrammed Sentry. [0/10]
Ethically Questionable
Conduct all of the questionable research experiments. [0/5]
Futile Resistance
Kill 10 enemies with Snarks. [0/10]
Gray Matter Propulsion
Headshot 20 enemies with the .357 Magnum. [0/20]
Hyper Saturation Conundrum
Drown in Lambda Core's coolant.
Inflammatory Actions
Kill a Headcrab using fire.
Kinetic Repulsion
Kill a Marine with their own grenade.
Mega Hertz
Kill 5 enemies with one grenade.
Nuclear Fishin'
Kill an Icthyosaur with either the Tau or Gluon.
Permeable Infrastructure
Use the alternative path in the Office Complex.
Premature Expulsion
Use an entire clip of Gluon ammo in one continuous shot.
Prophylactic Suggested
Get overtaken by a Headcrab's amble anterior.
Proverbial Tinkerer
Interfere with the alarm and laptop in Anomalous Materials.
Quantum Capacitance
Overcharge it anyway.
Rare Specimen
Send the Hidden Hat to Xen.
Remote Detonation
Kill a Barnacle with a Satchel.
Resonance Procrastinator
Refuse to insert the specimen into the Anti-Mass Spectrometer.
Unified Coupling Theorum
Help the Barnacle and Headcrab find true love. [0/10]
Universal Gravitation
Get killed by your own Snarks.
Best Answer
You can't yet.
Being "Greenlighted" in the movie industry (from whence the terms comes) and in Steam both mean that they've been accepted for further development. It doesn't mean that the game/movie is actually released and available for download / for watching in theatre, just that production with that company is moving forward and it very likely will be released at some point.
The Steam Greenlight page for Black Mesa shows that the game has been Greenlighted, meaning that it has received enough support from Steam users in the form of votes to go into production as a Steam-powered download. At the moment, there are only 10 Greenlighted games, among thousands of proposals on Steam Greenlight. (Zero games have been released through the Greenlight process yet (as of Sept 2012), which isn't surprising since the whole idea is new.)
How to get the game
I downloaded and started playing Black Mesa only two days ago, so the process is fresh in my mind.
To play Black Mesa, you need an installation of the Source SDK Base 2007 on Steam, which is free. To verify if you already have it, and to install it if you don't have it yet:
Then, download the blackmesa.zip file from the official homepage. I went with a Bittorrent download (because I guessed that my connection could handle more than I was likely to get from the site's direct-download link), and it downloaded in a bit under two hours (at an average of 1Mb/s).
Inside the zip is a
.7zarchive and a.exeinstaller. The installer found my Steam account, had it download and install the Source SDK, and then unpacked the files in the.7zarchive into the location in the Steamapps folder where Steam looks for Source mods. It handled this all automatically, which I must say is pretty slick for a mod. It then asked me if I wanted to launch Black Mesa right away, and notified me that it would show up in my Steam Library after I shut down and restarted Steam.All in all, it was a painless install. It will be even easier when it moves out of Greenlight and becomes a Steam Release game, but it can't get too much easier than it already is.