Synergy is a Half-Life 2 cooperation mod. It allows you to play through the singleplayer Half-Life 2 story with your friends. Synergy isn't just for Half-Life 2, that is, there are many other mods and maps that Synergy supports. There are mods such as
Minerva: Metastasis http://store.steampowered.com/app/235780
Dangerous World (http://www.moddb.com/mods/dangerous-world)
Half-Life 2: Calamity (http://www.moddb.com/mods/half-life-2-calamity)
Black Mesa (http://www.blackmesasource.com/ Support still VERY experimental!), and many, many others.

You must find a server, with or without people on it. Some servers I recommend are:

kana-chan's Synergy (Real Weapons)
10 max players
222.13.177.179:27015

Psycho Synergy Madness * HL2/Ep1/Ep2 * [Fast Respawn]
10 max players
71.201.240.188:27030

mucosmos.nl Eendracht : HL2 + EP1 + EP2 : votecar
8 max players
95.211.30.23:27015

And, of course, there are 10 official Synergy servers in Houston, Texas, and 2 in New York.

If you are looking to try something else, such as mods, or custom maps, these are some servers to try out:

The Hive -=THC=-
10 max players
50.97.113.106:27015

CIT Synergy | cit2.net
10 max players
5.135.139.193:27015

[V33R.CF] |Black Mesa: Source| |24/7 US-EAST| [INSTANT RESPAWN]
10 max players
74.102.226.194:27017

kana-chan's Hardcore Synergy (Real Weapons)
6 max players
222.13.177.179:27017

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If you would like to start your own server, see this guide:
http://steamcommunity.com/sharedfiles/filedetails/?id=359445849

Anyone! Synergy is all about playing with and meeting new friends.

Take a look at the community hub at:
http://steamcommunity.com/app/17520

And join the Steam group at:
http://steamcommunity.com/groups/synergy

As of December 2014, Synergy now has Steam Workshop support. Workshop will allow you to get custom maps and content at the click of a button. As of now, the Workshop is quite empty, but keep checking back, as there will be much more content to come from community members, or who knows, even you?

Synergy is all about having fun with your friends and other players, whether it is fighting Combine, or jumping across huge gaps in your scout car, or trying to figure out a hard puzzle, make sure you are having fun!