It's a little late - Metro: Last Light's Faction Pack DLC came out a couple of days ago - but this launch trailer gives you a good idea of the styles of play associated with each of the game's factions. Essentially: sneaky, snipery, and - er - hate-y, as you complete three missions as a Polis Ranger, a Red Line Sniper and a Reich Heavy. It never said they were nice factions.
The Faction Pack is the first of four planned DLC updates for Last Light. Other add-ons will include the Developer Pack, which will "give creative players some interesting tools with which to explore the world of Metro"; the Tower Pack, which is said to offer a "unique solo challenge to Metro veterans"; and the Chronicles Pack, which will bring more single-player missions to the game.
Metro: Last Light Faction Pack is out now, available for $4.99 / £3.99 / €4.99