I reach out to just about every person who trains for strength in my gym. I say hello and ask if they're getting stronger, ask about their goals. I invite them to some see a powerlifting competition if they seem interested. Two new guys are going to come and compete with me in February, and a few more will likely come and check it out.
Most people are intimidated or put off because people like their own space, pace, etc. in the gym and try to keep others out of their workouts. We try to reverse this, and foster a "the more the merrier" type of atmosphere. The strongest guy in the gym now comes in to work out with us, and this was a guy who typically left the headphones blasting, never making eye contact with anyone from the time he arrived to the time he left. Now he shows up all smiles and if one of us isn't around, he asks where we are.
The other day after deadlifts we were doing double overhand static holds for time in the rack, calling out the seconds and generally making it a competition, along with some cheering and jeering, etc. A guy I've never met just came over and asked "Can I get in on this?" We said yeah, man, and he did pretty decent, with all of us cheering him on. We went on doing this until I couldn't make a fist the next day. Workouts get harder when you're caught up in the moment.
I love the new, inclusive atmosphere in our gym and do everything I can to promote it. It needs no gimmick attached, just a willingness to step out of your comfort zone and approach those somewhat difficult-to-approach types. It pays off.