What if YOUR jaw hits the floor and YOU go off with someone else? 
You need to have a long chat with your FB, and discuss what you both want out of visiting a swingers club. Are you planning to just play together, or are you looking to join in with someone else / another couple, etc etc.
Bear in mind that you don’t have to do anything - you can just go and look. Generally, most people are friendly, and respectful, and understand that no means no, although there are pushy single guys that spoil things for those of us that aren’t… 
All ages, sizes and shapes go to singles clubs. Believe me, you won’t stand out!
What you can expect depends where you go. I’ve only experienced a couple of clubs, so can’t give you too many specifics, but generally, they will have a communal area, like a bar, changing rooms, and some “play rooms”. Some have dark rooms, glory holes, pools, hot tubs, saunas etc.
Wear something sexy. Be as daring as you feel!
Maybe something that you might have worn clubbing, and maybe take a negligee to change into? Just a suggestion.
As to where to go, it depends. I go to local clubs, as I’m not bothered if I run into someone I know, but you may feel differently. Fab has a great list of clubs, and you can always post something on the forums for feedback on a specific club.
I’d go in a bit later, as things don’t tend to liven up until after 10:30 ish, but your mileage may vary! 
I can’t answer what affect it will have on your relationship, sorry. It may get worse, it may fail, it may get 100 times better! - which is why communication is key.
Feel free to pm me if you think I can be of any more help.