Steam doesn't have the latest update (1.59, if you have Combined Operations or ArmA 2 Operation Arrowhead) available yet, but Dwarden (A BIS Superhero) is currently working to get it onto steam.
Until that happens, you can download the latest patch from this site, as it will work with a steam install. (The 1.59 patch is for Operation Arrowhead, if you don't have that, don't download it.)
Also, City Life isn't open to just everybody who clicks on their server, you would have to register on their website, get their TS Info, download their mod (over 1GB I think) and then they give you the password to play on their server. They tend to be a little nazi-ish (Godwin's Law is always right.
) and will ban you without a second thought if you act like an idiot in any way (atleast until they get to know you), because they all have jobs and they come on to play, not deal with people trying to annoy them/ignore rules.
I used to have the City Life website info somewhere, but it seems my Firefox deleted a bunch of my bookmarks. :/