Guilds: Guilds are better as mid-to-endgame activity, but many want to find a guild early on.
Mechanically, one applies for a guild by clicking the Guild button on the main (starting) game screen. You may flip through the list (random) or search a guild name in the text box. Enter the guild name exactly, it is CaSe SeNSiTiVe, and search does not provide close matches. You may apply to one guild at a time, applying to another voids a previous application. Pay attention to the response text below the request sent dialog box.. If the guild has openings, it will say "You are waiting for (guild)", and this will continue to appear until you are accepted or denied. If the guild is full, a request fails and it will say "Guild is full! Please choose another one."
Wait. You have to wait for the guild leader to find your application of otherwise contact you in return. They don't stare at the guild request screen 24 hours a day. ^.^
Looking for a guild: It is best to check the comments below the game and apply as requested. Some guilds simply want you to apply, others will request your Character Viewer (CV) or other comments or information be sent to a guild's FB group, or an officer's FB page, or the Cloudstone Friend's Group, for example. The better your level, home production, equipment, skill tree, and dedication/playing time, the better your chances are to get into and stay in a good, active guild.
Asking for a guild in the Tavern (Flying Pig) or other in-game chat: Always state which platform you are on (FB, Facebook), and ask the same of anyone offering a guild. This will save you time and frustration. There are even guilds with the same name on the different platforms, so don't take a familiar guild name as indicating you are both on the same server.