From my experience, after three decades of helping people get started in karting:
To get new people:
Advertising. Traditional sources, plus displays where people congregate (like shopping malls). Demonstrations at schools (our community college cooperated). Hand out free general admission passes to kids at school (stipulating that they must come with a parent if they aren’t 18).
Opportunities to try it out. Set aside a few days or nights where you have a few hobby class karts and safety gear available for people to try out. Have a few experienced racers there to give tips and answer questions. Let newbies run on the track by themselves or in very small strung-out groups so they aren’t stressed by more competition than they can handle. Practice days for non-racers who already have karts to try some laps (again in a low-stress situation), and have experienced racers who can give tips and help them sort out some problems.
Reward racers for bringing others. Give the racers a discount on their admission fee, and their non-racing friends get free admission. Don’t have to do this every race night, and you will probably more than make up the admission money if your snack / souvenir stand is any good, let alone if any of these people become racers.
To keep new people: (to me, “new people” are racers who have to learn to be competitive from scratch – not people who have experienced racing friends or relatives who give them a competitive advantage). They have to have fun, they have to feel like they have a fair chance, and they have to be able to afford to come back.
In my experience, people quit because:
Too expensive (entry fees and cost of equipment). Especially in kids' classes. You need to have AND ENFORCE rules designed to keep costs down. We did it by giving advantages to older (obsolete) chassis, dry shoe clutches, box stock motors, and narrow tires with no prep. Yeah, hard to police (especially motors and tire prep) – you need to get those racers to police themselves. KEEP PAYOUTS LOW so you can charge lower entry fees, and the high rollers tend to stay out because they can’t make a profit. Emphasis is the hobby class is for hobbyists and rookies.
Program too long. People get bored waiting hours and then getting fifteen minutes of track time, and their non-racing friends get even more bored. If you cannot limit your number of classes to get everybody satisfied with track time and also get done before bedtime then you either need to re-think your class structure or how you operate, or you need to break racing up into multiple days.
Rough driving / fights. Put a stop to it, even if you have to ban teams that bring a lot of people. They drive away more customers than they ever bring.
Tech enforcement problems / arguments. Need clearly stated policies and rules for every class, be able and willing to follow them no matter what, and show no favoritism.
Hobby classes need to be cheap starter classes. If racers get too good for this class, or if they want to buy fancier equipment, encourage them to move up to your other “regular” classes. NO money races in hobby classes. We used to have a small payout: winner got his entry fee back, second got half of what the winner got, and third got half of what second got. That was it. Collected more entry money than that? Apply it to making the track better, or buy stuff for bonus giveaways (for anybody), or lower entry fees. Don’t let racers talk you into allowing higher priced equipment in a hobby class – it gets out of hand very quickly.