Take the Lead
Be prepared to be the game master/leader/whatever. Download a couple of free rulesets ("Basic Rules" or "QuickStart Rules") - the legit versions, of course! - and get some idea of how some popular games work. Naming no names. But D&D Basic Rules are legit and free on the Wizards' site (e.g. only, Wizards of the Coast did not pay me for this post).
I know you said you're looking for existing groups - and feel free to ask for this explicitly in your efforts - but be aware that proactive is the only way to go.
Get Online, Take it offline
I agree with some of the other answers, find out what social media are active in your locale (and - crucially - social groupings, see next point) and post some offers of a beginners' game on there.
One jumping-on point could be the board and card games scene. Go along anyhow and just bring your print out of the [insert popular RPG] quick start. Mention you're looking for a group to join. There's a lot of overlap.
As others have said, put up a short note in your local games' store, comix store, youth club, anything public where you think you'll find some fellow players. Keep it simple, add some fun clipart and put a throwaway email address there for gaming purposes only in case you get emails that you don't want.
Be prepared to invest a little time into what amounts to "dating" gamers. All the online safety rules apply here. It's a good idea to suggest meeting up at a neutral public place e.g. the local game store to chat.