First thing firsts, if you want to experience local culture when traveling, stay away from tourist sites and tourist attractions. We all know that those experiences are far from truly experiencing local culture. Sure, you may want to explore the Colosseum in Rome or visit Boca in Buenos Aires--but think about it this way...when you visit New York City, do you really get a New York experience by staying in Time Square? Do as the locals do. Travel with as few plans, commitments and reservations as possible. Be your most uninhibited self.
Easiest way to get the local knowledge is from the locals. This is true. Most people are proud of their home and love to tell you about it. One trick is to go to a restaurant early, like so you are the only customer - the staff will talk to you. Ask your waiter, ask your cab drivers (use discretion here - cab drivers often get kickbacks for nightlife type activities), ask people you meet at the bar, or the cafe, or people you run into in the lobby of your hotel. Ask random people on the street. Rent places via AirBnB or Couchsurfing and ask your host. As long as you are polite and use good judgement on when you are asking someone (i.e., don't interrupt people) usually people are happy to help and make recommendations. Almost everyone wants visitors to enjoy their city / country and leave with a good impression.
Don't be intimidated by language barriers. Explore other forms of communications. Bring postcards from home to show and share. Draw pictures. Pantomime.
Be willing to try (nearly) anything. Food is a good example. Local "delicacies" may be intimidating, but you can pretty safely assume they aren't killing anyone.
Lastly, smile! People will respond best if you are approachable and polite. Well, at least this has worked for me!