Traveling like a local in Cuba is either an oxymoron, legally impossible, or will require a lot of time, patience, and humility. So while you may not be able to travel like a "local Cuban" 100%, there are a few ways to get a little closer to the local way of traveling.
Camiones/Hitchhiking in Cuba ("Pidiendo Botella")
This is my favorite way to get around because you don't have to plan it ahead of time and it's one of the most affordable ways. You usually go to a long distance bus station and wait around for the trucks or big buses to drive by. They will yell which way there are going, and you yell or wave frantically for them to notice and stop for you. This is how I got from Las Tunas to Havana for. And it's how I got into a bus from Bay of Pigs to Havana for $1. You cannot book this ahead of time. The other option is straight hitchhiking (which is very similar), you wait by the main highways (autopistas) where you'll see lots of Cubans waiting around for a bus, truck, or anything that will pick them up.
Where to Meet Cubans & How to Make Cuban Friends
First, befriend Cubans "without interest" and not jineteros. Jineteros are hustlers, scammers, scrubs (like the TLC song). They have long cons (marriage for visa) and tons of short cons (asking for you to pay for their drinks, selling you fake cigars, trying to take you to a restaurant/bar for a commission, asking you for money, etc).
Where to meet local Cubans
Malecon - It's free and where many Cubans hang out with their Cuban friends and have fun. Chess & Dominos - Take out a chess board/pack of dominos on the Malecon or a park and invite a Cuban to play with you. Sports - Bring your soccer ball to a park or a volleyball to Playa Santa Maria (beach) and invite local Cubans. Free local event - Ask around and you'll see there are tons of free or very low-cost events in Cuba. From fashion shows to famous musicians playing on the streets or government venues, you'll be in the midst of tons of local Cubans to meet. Playa Santa Maria - A local favorite beach, here you will see a mix of tourists and Cubans hanging out with each other.
Hair Salon - In Cuba, this is a full day affair where 5+ women congregate in a living room over cafecitos and talk about life while the hair stylist takes turns simultaneously doing everyone's hair at the same time. But for a balayage, cut, and a blowout, you can't complain. Click here to visit a Cuban hair salon in Havana.
Dating in Cuba: Dating a Cuban Man/ Woman
This one is tricky. As a foreigner in Cuba, you have to take the same precautions a very wealthy person takes when trying to find a genuine relationship with another person of "less means". You may wonder, does your Cuban lover like you for you or do they like you solely for your wallet/passport privilege as a ticket out of Cuba?Like dating anywhere else in the world, sometimes your prospective mate is only attracted to your status and money. But in Cuba, as my University of Havana professor put it, a tourist to many Cuban jineteros is like "seeing a pot of gold". Don't be fooled when your Cuban jinetero lover takes you to meet his/her entire family on the second date. The family is probably in on the long con and cheering on the arrangement. They benefit from this just as much as your Cuban jinetero!