Travel is often more rewarding when you experience a new place from a native perspective. Here are some tips for creating as authentic a local experience as possible.
Research The Culture, Traditions & Daily Life
Before jetting off, take some time to educate yourself on the culture, traditions and daily lifestyle of your destination. This will deepen your appreciation of the experience and guide your behaviour so that you don't offend or disrespect natives. Also, try to get a sense of the general pace of life, whether it is more relaxed or faster paced and what some of the daily life looks like for residents.
When I was in Rome, for example, I learned about apertivo, which involved going for a drink and light snacks in the evening at a restaurant or bar, and then a stroll before having a late dinner (by our standards).
Find out where residents like to eat and drink, then respectfully check the spots out for yourself. Hopefully you'll end up surrounded by locals who can give you more tips for making the most of your time in their area. If possible, familiarise yourself with some of the native language(s) so that it will be easier to get to know locals.
Avoid Events & Places That Mostly Cater To Tourists
A lot of the highly recommended activities aren't actually the ones locals spend their time on. In fact, in those touristy areas, the only locals you'll interact with will be working! Trying to break down that barrier can be made easier by finding people in the setting in which they're most relaxed, like a local bar or other hangout.
When I was living in Kyoto, I went to an onsen with a group of students from a nearby university. Because they were familiar with the area, they knew which one to go to that would be free of gawky tourists, which lead to a much more authentic and deep experience for me.
Connect With People Who Can Be Your Behind-The-Scenes Guides
The easiest way to find experiences like the onsen I went to is to establish connections with locals who are willing to be your guides. If cultural exchange programs aren't an option for you, as they were for me, consider using apps and sites to help, like Vayable or Like A Local. If you've got an iPhone, try out asknative, which aims to get answers to your questions from -- surprise -- natives.
If language barrier proves to be an issue, try using your mobile device to help communicate. While many people are delighted to freely share advice with you so that you can experience their country from an authentic perspective, do be wary of scams.
Stay In An Area Where The Locals Live
Use sites like Airbnb or HomeAway to rent locals' homes. That way, you can surround yourself with residents as they go about their daily lives and hopefully experience some of it yourself. If you get a good host, they will leave you recommendations of places to check out.
Another great and inexpensive way to meet locals is to earn your lodging through work. I know someone who recently did this in Japan, and during breaks in the workday his host took him out on a small sailboat to dive for shellfish to eat. This opportunity to experience a resident's daily routine isn't something that is commonly offered to tourists; by essentially living with a resident, you can get this kind of access to local life.
Remember that this is about skipping the tourist traps and building relationships with locals who are willing to give you a glimpse into the life of the area's citizens. Arm yourself with knowledge beforehand so you can be respectful and able to communicate, steer clear of events and spots where tourists congregate, and keep an open mind.