RED dot - The mod isnt installed or it is either corrupt or the wrong version of the mod is loaded compared to the version running on the server. The mods you need will be listed here and have either: Ignore the ones for the official DLC (Helicopters, Marksman, Carts etc) and check the mods listed below them.
Single click the server in the list and look at the bottom right of the server browser screen, you will see a list of mod names with either red or green dots next to them. To find out what you need to play, look at the server you want to join in the server browser. Shout out to clan for the great guys that operate the helpdesk in their Teamspeak. Most servers list the mods required in their name on the server browser or you can look up their website, most of the decent servers will have details and instructions for joining on their website as well as links to the mods needed. This is the major benifit in using a third party launcher over doing it all yourself, but once you have the hang of it its better doing it yourself IMO. The most confusing part of getting into modded servers in Arma for new players is identifying which mods and versions are required for the server you wish to play on.